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STORAGE BATTERIES

OK TIIJ5

'•■,.

•J^^y^

THE MACMILLAN COMPAl^Y

NBW YORK • BOSTON • CHICAGO
DALLAS • SAN FRANCISCO

MACMILLAN & CO., Limitbo

LONDON • BOMBAY • CALCUTTA
MBLBOURNS

THE MACMILLAN CO. OF CANADA, Ltd.

TORONTO

STORAGE BATTERIES

THE CHEMISTRY AND PHYSICS OF THE

LEAD ACCUMULATOR

HARRY W;' MORSE, Ph.D.

AHS18TANT PROFE880K OF PHYSICS
IN HARVARD UNIVERSITY

Ncto gorfe
THE MACMILLAN COMPANY

1912

All right* reserved

OOPTXXOBT, 1918,

By the MACMILLAN COMPANY.

Set up and electiotyped. Published February, 19x3.

Nortsoob 9iYM

J. 8. Cashing Co. — Berwick A Smith Co.

Norwood, Mass., U.S.A.

CONTENTS

CBAPTXB

I. Introductory and Historical

II. SoMR Electrociikmical Fundamentals

III. About Ions ....

IV. The Fundamental Cell-reaction
V. The Active Ions

VI. Some Pertinent Physical Queries

VII. Energy Relations .

VIII. Reactions at the Electrodes

IX. Charge and Discharge .

X. Capacity ....

XI. Efficiency ....

XII. Internal Resistance

XIII. Physical Characteristics

XIV. Formation of Plant!?: Plates
XV. Paste Plates .

XVI. Diseases and Troubles .

XVII. Some Commercial Types

XVIII. Accumulators in General

Appendix

PAQU

116

141

148

172

179

194

205

225

246

255

STORAGE BATTERIES

CHAPTER I

INTRODUCTORT AND HISTORICAL

1. Into our present age of power, where we reckon
by thousands and tens of thousands of kilowatts,
there has come down from a previous era one single
form of the galvanic cell which retains sufficient
commercial importance to be worth consideration in
'connection with modern power plants and modern
power operation. This is the lead-sulphuric acid
accumulator. It was invent<3d and perfected in the
heyday of galvanic cells — at a time before the dy-
namo and the electric motor had any technical im-
portance. In our own laboratory, hidden away in
the attic where cast-off things are stored, lie the
remains of the big Bunsen cells which were once the
source of our heaviest currents and with which the
remarkable phenomena of current electricity were
shown to classes and in public lectures in tliose
days. These same cells were used to charge small
storage cells of the original Plante type — mere strips

B 1

8TOBAGE BATTERIES

of lead, separated by soft rubber insulators and rolled
into spiral form ; then formed with the aid of the
primary cells, by a series of reversals, until the plates
attained a certain capacity. One of these cells is
shown in Figure 1. With these storage cells, which
have low resistance and high current-giving capacity
even in comparison with the large Bunsen cells, the
most wonderful experiments could be
performed — experiments which are to
. us now so commonplace and so much a
part of our everyday life that their de-
scription brings a smile from the high-
school boy who has studied physics and
chemistry. These cells would run an
arc light for several minutes; heat
small platinum wires to the melting
' il'l'i ' ' M'i poi'i*'; provide current for electro-
^^^^ ^^^ magnets of power enormous for that
Fio. t.— oriEiiial time. It was the duty of the labora-
typc of Planw j^j^y asgigtants to set up the battery
(About J full "^ Bunsen cells. Huge zinca in dilute
SIC.) sulphuric acid and great blocks of car-

bon were armnged in glass jars with porous cups,
and from this fuming source the storage cells were
charged all day, to be used the day following in
demonstrations of the power of the electric current.
After the charge was fiuished the big Bunsens were
taken apart and cleaned up, then stored away until

INTRODUCTORY AND HISTORICAL 3

the time for the next lecture on electric currents
approached.

These early Plante batteries were so arranged that
they could be easily thrown into parallel connection,
and in this way they could be charged from the
Bunsen battery of a few large cells. We still use
one of these batteries of 20 cells, dating from the
early eighties or earlier. After charge was com-
plete the simple mechanism permitted all the cells
of the set to be connected in series by simply turn-
ing the handle through 90°, and clips were provided
to show the melting of wires of various metals by
the current.

The current which could be drawn from these
small sets of storage cells reached its maximum at
forty or fifty amperes — an enormous value then, a
mere bagatelle now, for we have electrolytic cells
and electric furnaces which require tens of thou-
sands of amperes for their operation. Since then
lead cells have grown in size along with everything
else electrical, and I have seen large batteries which
can furnish thirty or forty thousand amperes for a
short time and ten thousand for several minutes of
discharge.

2. No one of the very numerous primary cells
which have been devised and patented has ever
reached commercial importance for the- heavier work
of the present period, though a few have survived to

4 STORAGE BATTERIES

do the lighter tasks. The Leclanche and numerous
similar types are used in large numbers for bell-
ringing installations and similar open-circuit appli-
cations. And the dry cell has a very large and
distinct place of its own in sparking batteries for
motor cars and boats and everywhere that internal
combustion engines are used. Certainly well over
ten million of these little primary cells are made and
used each year in the United States.

From the beginning of the nineteenth century
until the early eighties was the era of the primary
cell. Then came the dynamo and the motor, ac-
companied by improvements in our main prime
source of power, — the steam engine, — and the stor-
age cell has grown along with all of these in a
somewhat subordinate place. It is a mere assistant,
to be called on for temporary aid in time of need,
either to help over an ugly peak in the load on the
prime source, or as insurance to be called in when
the main source is disabled for a short time, and its
aid is often quite invaluable under these conditions.
As a real factor in the problem of prime power
sources it has of course no place at all.

There is not much value in prophecies about scien-
tific or technical things and no particular credit is
due the prophet who utters them. Nevertheless, I
feel impelled to say that I believe the day of the
primary -cell will come again. From every funda-

INTRODUCTORY AND HISTORICAL 5

mental and theoretic point of view we must admit
that it should be possible to make a primary galvanic
cell which should be more efficient than a steam
engine can possibly be ; more flexible as a primary
source of power; a better appliance in every way.
y 3. At first glance a lead-sulphuric acid storage
cell seems a very simple and uninteresting sort of
machine. It is only a plate of lead and a plate cov-
ered with lead peroxide, dipping into rather concen-
trated sulphuric acid. But for those who make
them and those who care for them in service they
become much more complex and puzzling, and worth
careful consideration. As an integral and essential
part of many power arrangements they are of inter-
est to the engineer and as a complex of puzzles and
problems they demand attention from the electro-
chemist and the physicist. Many books have b^en
written about them, some purely scientific and others
nearly purely technical. As far as the fundamental
chemical reaction is concerned we seem to be on
pretty firm ground, and there is every reason to be-
lieve that we know how the cell works. But there
is still plenty of room for speculation and research
on the more minute physical changes and a good
many questions on such important matters as forma-
tion, cementing of pastes, sulphation, and life under
various conditions cannot even now be answered
very clearly.

6 STORAGE BATTERIES

A very large number of combinations have been
suggested for storage battery purposes since Plante
began to study his cell in the late fifties, but until
within the last few years no one of them has seemed
able to meet the rather difficult* and peculiar require-
ments. Now comes the Iron-Nickel Oxide-Alkali
combination as applied by Edison in this country
and Jungner on the continent of Europe, and this
type seems destined to find a place of its own in
light traction work. But by far the greater part of
all storage battery plates now made are descendants
of the original Plante type — hardly recognizable
with their highly developed, ribbed, or corrugated
surfaces, and formed in the factory by rapid methods,
but still " Plante " plates. We have in active use
in our own laboratory a unique battery which harks
back to the earliest form. It has twenty thousand
cells, made of test tubes, and the plates are merely
corrugated strips of lead. It is used to give the
small currents necessary for vacuum tube and spark
work, and it was formed by the old method of re-
versals (see page 179) until it reached the needed
capacity.

4. Faure was the inventor of the " paste " plate,
and this seemed at first so great an improvement
that prophets were not wanting to predict that the
older type, with its greater weight, comparatively
small capacity, and higher cost, would be completely

INTRODUCTORY AND HISTORICAL 7

ousted by the new invention. These prophecies
have not been fulfilled. The paste plate has been
gradually relegated to traction work and to duty
where weight is the important factor, and the plates
which are direct descendants of the Plante originals
do the really hard work. It took much experience
and expense to reach the decision that the Faure
plates could not compete in the more strenuous posi-
tions, but now we seem to appreciate fairly well the
limitations of both types.

5. As the storage battery developed to a point
where it 'could handle real power loads, there came a
time when its powera were somewhat overestimated.
It was suggested for many positions where it would
have been quite unfit for the work — for farm pur-
poses, for motor cycles, and even for airships. For
long-continued discharge, where it must take the
place of the prime source of power over considerable
periods of time, the storage battery is often a cum-
brous and expensive substitute for the source itself.
But for many kinds of work, and especially where a
very large amount of power is needed suddenly or
for short periods, the battery is the ideal machine.
In many modern plants the load fluctuations are very
great — a thousand per cent or more, and this within
a fraction of a minute. No mechanical arrangement
can absorb this and regulate the load on the power
source in a satisfactory way. But a storage battery

8 STORAGE BATTERIES

can, for there is hardly a limit to the rate at which
large-surface Plante plates can be discharged or
charged without injury.

In certain classes of work — in submarines, as a
source of under-water power, for example — the bat-
tery is an absolute necessity. In the regulation of
irregular loads it is of the utmost importance, and in
emergency or "stand-by" work as well. Car and
train lighting systems demand its use. It has proven
itself economical and efficient in traction work, espe-
cially for electric road vehicles.

Study of the storage battery calls for attention to
two rather distinct viewpoints — one chemical, the
other physical ; and these will be found of nearly
equal importance. The questions about the funda-
mental reactions, and many others as well, are purely
chemical. Questions about the life of the cell, and
its behavior in service, are nearly purely physical.
In manufacture or operation the chemical side must
be kept in mind, but the anatomy and physiology
(and sometimes the pathology, too) of the individual
plate are matters of prime importance. Underlying
all, we will need as a foundation for study the funda-
mental ideas and laws of general electrochemistry.

The following chapters are based on lectures which
have been given for the last few years at Harvard
University. In the course the work on storage cells
is preceded by study of the general theory of gal-

INTRODUCTORY AND HISTORICAL

vanic cells, and the simplest of this theory has been
included in this book. No attempt has been made
to give any of the detail of storage battery engineer-
ing, but only to introduce the reader to the peculi-
arities of the cell itself.

CHAPTER II

SOME SLSCTROCHSMICAL FUNDAMENTALS

6. Theoretically any chemical reaction whatever
which takes place of its own accord can be so
coupled and arranged that it will work as the source
of energy for a galvanic cell. Practically there are
difficulties which exclude a large percentage of the
known reactions of chemistry from such service. It
is also true that a great many of the combinations
which have practical value as primary cells can be
considered theoretically reversible enough to be used
Jis storage cells. As a matter of fact, only a very
few of the cells which have been used or thought of
are chemically and mechanically reversible enough
to fit them for actual use as storage cells. In some
Ciises the fault is in the reaction itself, and the cell is
not chemically reversible. In others, the reaction
reverses smoothly enough, but the materials of the
cell do not go into and out of solution well. Here
the fault is a mechanical one. As far as the general
theory is concerned, we must choose fundamentals
which fit all the cases, even those which cannot be
realized practically.

SOME ELECTROCHEMICAL FUNDAMENTALS 11

7. Faraday's Law. — We have one general funda-
mental electrochemical law, which apparently fits
every case, and which brings order of the simplest
kind out of what at first appeared to be a most cha-
otic mass of unrelated material. This is Faraday's
law, and it states the relation between the quantity
of material used up in a galvanic cell and the quan-
tity of electricity which can be obtained from it.

This law says : —

The amount of each substanoe which takes part in an
eleotrochemioal reaction is proportional to the quantity
of electricity which passes through the circuit.

And when various substances enter an electrochemical
reaction, their amounts are proportional to their chemical
equivalent weights.

Numerically, and in terms of a unit later to be de-
fined : —

96,540 coulombs pass through the cell and the external
circuit with each gram-equivalent of each substance
involved in the reaction^

8. Faraday's Definitions. — This law applies to elec-
trolytes. Faraday himself felt the necessity of a
careful set of definitions for the new ideas involved
in this law and its application, and no one has since
given better ones, so we shall iise them wherever it
is possible to do so.

To quote Faraday ("Experimental Researches,"
Series VII, 1834): —

12 STORAGE BATTERIES

"... In place of the term pole, I propose using
that of Electrode, and I mean thereby that substance,
or rather surface, whether of air, water, metal, or any
other body, which bounds the extent of the decom-
posing matter in the direction of the electric current.
. . . The anode is therefore that surface at which
the electric current, according to our present ex-
pression, enters. It ... is where oxygen, chlorine,
acids, etc., are evolved; and is against or opposite
the positive electrode. The cathode is that surface
at which the current leaves the decomposing body,
and is its positive extremity ; the combustible bodies,
metals, alkalies, and bases, are evolved there, and it
is in contact with the negative electrode.

"... Many bodies are decomposed directly by the
electric current, their elements being set free ; these
I propose to call electrolytes. . . .

" Finally, I require a term to express those bodies
which can pass to the electrodes. ... I propose to
distinguish such bodies by calling those anions which
go to the anode of the decomposing body, and those
passing to the cathode, cations, and when I have
occasion to speak of them together, I shall call them
ions. Thus, the chloride of lead is an electrolyte, and
when electrolyzed evolves the two ions, chlorine and
lead, the former an anion, and the latter a cation. . . ."

Figure 2 shows the different parts of a cell as
Faraday defined them.

SOME ELECTROCHEMICAL FUNDAMENTALS 18

These definitions of Faraday's were made with the
greatest care, but since they were formulated, rather
careless use has sometimes been made of them. Note
the term anode. It is the surface where the current
enters the cell, and Faraday meant just exactly this
whenever he used the word. The plates of a cell are
not anode or cathode in this sense, but the surface
between plate and
cell solution is.

There will often be
occasion to retain

this strict meaning
of the word.

Again, an electro-
lyte is the body
which carries the
current and which

MRECnON
OF CUMICNT

iflDTfiooc ELeemoioE

KANODO (DATMOOd

ANION

CLCCTROLYTE

CATHION

Fio. 2. — The parts of an electrolytic cell.

is at the same time decomposed by it. In this sense
a dry salt is not an electrolyte, but a solution of a
metallic salt, or a molten salt, belongs in this class.

9. Electrical Units. — Before we can apply this law
of Faraday's we should review a few more electrical
definitions. In what is called the practical system,
we use as unit of quantity of electricity one conlomb.
This is derived from the unit of current, the ampere,
and one coulomb is the quantity of electricity which
passes through a circuit altogether, when a current
of one ampere has been flowing constantly for one

14 STORAGE BATTERISa

second. These units have been fixed with reference
to the magnetic effect of a current and not specially
with reference to Faraday's law. It is, however, an
easy calculation to state them in terms of units which
bear directly on electrochemical effects. Suppose we
have in the circuit an amperemeter which measures
the current in amperes. We keep the current con-
stant and note the entire time during which it flows
through an electrolytic cell in which silver is being
deposited from silver nitrate solution. We will find
that one ampere flowing for one second deposits
0.00111775 gm. of silver. The equivalent weight
of silver is in this case the same number of grams as
its* atomic weight, and lias the value

107.88 gm.

The number of coulombs required to deposit this
weight of silver is then

107.88

0.0011175

=s 96,540 coulombs.

This same number of coulombs will deposit the
equivalent weight of any other metal which can be
electroplated in the same way, and it is the electro-
chemist's unit of quantity of electricity.

If the silver were to be used in a galvanic cell as a
source of power, exactly the same relation holds be-
tween the weight of silver and the quantity of
electricity — 107.88 gm. of silver always travels

SOME ELECTROCHEMICAL FUNDAMENTALS 15

through an electrolyte and dissolves or precipitates
at the electrode in company with 96,640 coulombs.

Silver ion is univalent, and the equivalent weight
is the same as the atomic weight. In most of its
reactions, chemical and electrochemical, copper
forms a bivalent ion. This means that in company

Fia. 3. — Diagram of apparatus to show Faraday's law.

with the atomic weight of copper (63.6 gm.)
twice 96,540 coulombs pass through the circuit;
so the equivalent weight of copper is 31.8 gm.,
and this is the electrochemist's unit weight of copper.
10. Experimental Arrangement for Faraday's Law. —
Figure 3 gives diagrammatic representation of an
experiment to illustrate Faraday's law. Current
is supplied by the battery A and passes first through
the tangent galvanometer B^ which measures it, and
then on through the various cells in which electro-

16 STORAGE BATTERIES

chemical reactions take place. In (7, a molten salt,
silver chloride, for example, is decomposed. 2)
might represent a copper ooulometer, in which copper
is dissolved at one electrode and precipitated at the
other. The same arrangement might be used for
many other metals. JS is one form of silver
coulometer, and here the current enters at a silver
anode, which goes into solution, and leaves the cell
at the surface of a platinum crucible (cathode) on
which silver is deposited. The electrolyte is a
strong solution of silver nitrate. Last in the row
is a gas coulometer jP, containing dilute acid or
alkali as electrolyte and having platinum electrodes.
Oxygen gas is formed at the anode, the electrode
where the current enters the apparatus, and hydro-
gen gas is evolved at the other electrode.

Suppose we have sent a constant current of one
ampere through the circuit for 96,540 sec. We have
weighed the electrodes before and after the passage
of this current, and we have measured the volumes of
the two gases produced. We should find : —

1. At (7, 107.88 gm, of silver dissolved from the
wire at which the current entera the cell and the
same weight of silver deposited on the other wire.
The electrolyte remains unchanged.

2. At 2>, 31.8 gm. of copper dissolved at one plate
and precipitated at the other. No change in the
electrolyte.

SOME ELECTROCHEMICAL FUNDAMENTALS 17

3. At E^ the same amounts of silver dissolved and
precipitated as in (7.

4. At -F, 8 gm. of oxygen formed, or 5.6 1. if
measured at 0*" C. and 760 mm. pressure, and at the
other electrode, 1 gm. of hydrogen, having a volume
of 11.2 1.

6. Inside the cells at -4., there will have been
exactly equivalent effects, and they will be the same
in each cell. Whatever the materials of the anode
and cathode, equivalent weights of each will have
entered into reaction, for as far as the application
of Faraday's law is concerned, it makes no difference
whether work is performed as the result of a reac-
tion, or must be performed from without in order to
make the reaction take place. The law describes
every electrochemical reaction, and has been shown
to be as exact as any law we have.

11. Praotioal Application. — Let us examine some
applications of this law. A great deal of copper is
purified in this country by an electrolytic process.
It is interesting to calculate the quantity of electric-
ity needed to deposit a pound of copper in this way.

1 lb. = 453 gm.

96,540 coulombs deposit 31.8 gm.

We therefore need

453

31.8

X 96,540 = 1,376,000 coulombs per pound.

18 STORAGE BATTERIES

Since an ampere is 1 coulomb per second, it will
require

' ^^ ' — = 382 ampere-hours
3600 ^

to deposit a pound of copper in a single cell. 382
amperes deposit 1 lb. of copper per hour in a single
cell, and if we wish to obtain a ton of copper per
hour in such a cell, it would take a current of nearly
760,000 amperes to give the desired result. As a
matter of fact cells of this size are never used. It
is better to arrange a number of cells in series, so
that the current flows through one after the other
and produces the same effect in each. The yield of
copper is then to be found by multiplying the yield
per cell by the number of cells.

The atomic weight of lead is about 207, and
it is formed from a bivalent ion, so the equiva-
lent weight of lead is 103.5. Rather more than
three times as much lead as copper is deposited by
the same quantity of electricity. The calculation is

453

X 96,540 = 422,000 coulombs per pound of lead.

103.5

12. Electrolysis in the Daniell Cell. — In the Daniell
type of primary cell the chemical reaction is a very
simple one : Copper is deposited as metal from cop-
per sulphate solution ; zinc (metal) passes into solu-
tion as zinc sulphate.

Zn + CuSO^ = ZnSO^ + Cu.

SOME ELECTROCHEMICAL FUNDAMENTALS 19

The reaction is indicated in the diagram of Fig-
ure 4.

How many ampere-hours can we get from a Daniell
cell per pound of zinc ?

The atomic weight of zinc is 65.4, and it acts as a
bivalent ion, so we will get 96,540 coulombs from

POROUS

1— ^-— ^^— rvnwv9 1

PlMrriTION CObPER

65.4

FiQ. 4. — Diagram of the reaction in a Daniell cell.

= 32.7 gm. of the metal. A pound is 453 gm.

Per pound of zinc we can therefore obtain
453

32.7

X 96,540 = 1,337,000 coulombs.

and since an ampere-hour is 3600 coulombs, one
pound of zinc will give 372 ampere-hours.

We can get this same number of ampere-hours per
pound of zinc in any galvanic arrangement whatever,
and it requires the same number to deposit a pound
of zinc electrolytically from its solution.

20 STORAGE BATTERIES

How much copper sulphate must we supply dur-
ing this time to keep the copper side of the Daniell
cell active ?

Its formula is CuSO^ -f 5 H^O, and the total weight
equivalent to 65.4 gm. of zinc is therefore 249 gm.
Copper ion passes through a bivalent step in its
deposition as metallic copper, so it requires ^|^ =
124.5 gm. of "blue vitriol" to give 96,540 coulombs.
To furnish 1,337,000 coulombs we must use

^^?^y?^ X 124.5 = 1725 gm., or 3.8 lb.
96,540 ^

'Since all our electrochemical reactions are really
only chemical ones arranged in such a way that they
furnish or require a current of electricity, we could
calculate the amount of copper sulphate needed for
our run with the Daniell cell directly from the pre-
ceding figure for the deposition of metallic copper in
the purification process.

A pound of blue vitriol contains -—^ = 0.255 lb.
^ 249

of copper, and we found that it required 382 ampere-
hours to deposit a pound of copper. The same
quantity of electricity will pass through the Daniell
cell with a pound of copper, and to get 1,337,000
coulombs from the cell we must deposit

1,337,000 ^ Q^o 11 f
g^^^^ = 0.9.21b. of copper.

SOME ELECTROCHEMICAL FUNDAMENTALS 21

This amount of copper is contained in 3.8 lb. of blue
vitriol.

13. Electrochemical TTnits. — It is evident that the
96,640 coulomb unit which the electrochemist is
obliged to use is a rather cumbrous one and leads to
large numbers. If we had the choosing of our own
unit we would of course make 96,640 coulombs = 1
electrochemical unit of quantity of electricity, and
then the calculation for copper would look like
this : —

63.6 g. Cu '^ 2 units,
1 lb. copper '^14.24 units,

and for zinc it would be equally simple. But elec-
trochemistry is not a big enough branch of science
to be able to dictate units to the dynamos which fur-
nish the current, and we must be content to accept
the electrical engineer's unit.

In every case it is necessary to know the complete
and exact chemical reaction with which we are deal-
ing before we can apply our law, for it very often
happens that metals carry different multiples of the
unit quantity of electricity with them in different
chemical reactions, and they sometimes complicate
things still further by changing the number of units
carried as the concentration of the solution from
which they are deposited is changed. But if we
arrange to have the conditions in the cell constant

22 STORAGE BATTERIES

and have once found the correct chemical reaction,
the law can always be applied without fear of error.
14. Electromotive Force. — Faraday's law gives a
complete statement of the quantity of electricity
which accompanies the reaction of gram-equivalent
weights of various substances in any galvanic com-
bination or electrolytic cell. But it can tell us no
more than this. It says nothing about the amount
of work we can do with this amount of electricity,

nor about the amount of work we must do to cause

the separation of a gram-equivalent of a metal from
solution. The driving force of the chemical reaction
and the corresponding electromotive force of the cell
are specific for each reaction and cannot be calcu-
lated by any inclusive general law. The driving
force is called the chemical potential of the reaction,
and it can be very conveniently and accurately
measured by coupling the reaction into the form of a
galvanic cell and measuring the electromotive force.

Very early in the development of galvanic elec-
tricity Volta found that the various metals could be
arranged in a series, such that the most favorable
combinations for producing current were to be made
by choosing metals as far apart as possible in the
series. Better results were obtained from cells using
zinc and copper than from those using iron and copper,
or zinc and tin. We know now that not only the
metal, but the whole reaction must be taken into ac-

SOME ELECTROCHEMICAL FUNDAMENTALS 23

count, but the " Voltaic series of the metals," as it is
called, gives an approximate view of the matter.

It was found very early that more work could be
obtained from a pound of zinc in a cell where copper
is deposited at the cathode, than from a cell where
iron is used in the same way. The same quantity of
zinc is used up in each case, and since we get different
results in the various combinations, there must be
some other factor of importance and some other law
besides Faraday's to be considered.

Suppose we have a very large Daniell cell, where

the reaction

Zn + CuSO^ = Cu -f ZnSO^

is taking place. We choose a big cell in order that
we may send 96,640 coulombs through it without any
danger of changing the concentrations in the differ-
ent parts of the cell. When this quantity of elec-
tricity has passed through the cell, 32.7 gm. of zinc
have gone into solution at th^ anode and have become
zinc ion. During this same time 31.8 gm, of cop-
per ion have changed into metallic copper. The
SO4 part of the reaction has not been affected at all.
Electrochemically we could write the reaction

Zn^et + Cu++ = Zn++ -h Cu^et-

15. Ions. — The small sign + indicates that the sub-
stance carrying them is an ion and that it moves
toward the cathode — it is a cation. Two of them

24 STORAGE BATTERIES

indicate that this particular ion carries with it per
gram-atom twice the unit quantity of electricity
(2 X 96,540 coulombs). The SO^ ion (SO^— ), which
remains unchanged in this particular case, carries
two times the unit quantity also, but toward the
anode. It is an anion. And in chemical parlance
both of these are divalent ions.

Now suppose we connect the cell with an external
source of current and send 96,540 coulombs through
it in the opposite direction. 32.7 gm. of zinc will
deposit on the zinc plate, — now the cathode, — and
31.8 gm. of copper will go into solution at the copper
plate, — now the anode. By the time we have sent
our unit quantity through the cell it has been com-
pletely restored to its original condition. The case
of the Daniell cell is theoretical rather than practical,
for zinc does not behave very well when it is forced
out of solution. It grows in sponge and trees and
often reaches across to the other plate and short-
circuits the cell. But we have chosen our cell so
large that this does not bother us, and the Daniell
cell can be considered completely reversible in its re-
actions. It might therefore be used as an accumu-
lator.

16. Other Electrical ITnits. — Besides the coulomb,
we have been supplied with two other units, and these
fortunately fit electrochemical needs pretty well with-
out requiring so many figures. One of these is the

Ampere

Volt

(«)

Joule

O")

80ME ELECTROCHEMICAL FUNDAMENTALS 26

volt, the unit of difference of potential, and the other
is the ohm, the unit of resistance.

The following terms and relations are important: —

Coulomb (j^) Quantity of electricity.

Current.

Difference of potential.
Energy.

1 volt-coulomb = 1 joule.

watt = rate of furnishing energy.
1 volt-ampere = 1 watt.
1 joule per second = 1 watt.

3600 coulombs = 1 ampere-hour.
1000 watts = 1 kilowatt, KW.
746 watts = 1 horse power, H.P.
746 X 3600 joules = 1 horse-power hour, H.P.H.

Beside our units we can also get instruments for
measuring them from the electromagnetic branch of
electrical science. If we borrow a voltmeter from
our neighbor, the electrical engineer, and apply its
terminals to our Daniell cell, we measure what is
called its electromotive force in volts. The volt-
meter reads about 1.1 volts.

17. Electrical Energy. — We can now calculate the
electrical energy obtainable from this cell. By ex-
pending 32.7 gm. of zinc and 31.8 gm. of copper ion
we can expect to get 1.1 x 96,640 volt-coulombs
(joules) with which to do useful work outside the

26 STORAGE BATTERIES

cell. If we are sending current through the cell in
the opposite direction, we can reverse the reaction
and return the cell to its original condition by an
expenditure of the same amount of work.

We can now calculate both work and power.
How many horse-power hours can be obtained from
a Daniell cell per pound of zinc ?

32.7 gm. of zinc give

1.1 X 96,640 = 106,300 joules.
1 H.P.H. is

746 X 3600 = 2,683,000 joules.
1 lb. of zinc will give

^ X 106,300 = 1,472,000 joules.
32.7 ' ' J

1 lb. of zinc will therefore give

14||S= 0-55 H.P.H.
2,683,000

Or, we must use a little less than 2 lb. of zinc per
horse-power hour.

Other forms of zinc-consuming cells were formerly
much in use, and some of these had electromotive
forces as high as 2 volts. One of these would re-
quire only

-j- lb. of zinc to produce 0.56 H.P.H. ,

and we would need only 1.07 lb. of zinc per horse-
power hour in the case of one of these cells.

SOME ELECTROCHEMICAL FUNDAMENTALS 27

Besistanoe. — The unit of resistance has an inter-
esting and simple relation to the units of current
and voltage. What is called Ohm's law states

, . electromotive force in volts

current in amperes = ;— ; — =

resistance m onms

Or, an electromotive force of 1 volt will send a cur-
rent of 1 ampere through a circuit having a resist-
ance of 1 ohm.

A column of mercury 106.3 -cm. long and one
square millimeter in cross-section has a resistance
of 1 ohm. A good-sized copper wire has a resistance
of an ohm for a length of a thousand feet or so.

18. If it is desired to furnish 0.5 H.P. from a
single Daniell cell, at what rate must zinc dissolve ?

0.6 H.P. is 373 watts (volt-amperes) (volt-cou-
lombs per second). Our cell gives 1.1 volts and
must therefore give a current of 349 amperes (349
coulombs per second).

32.7 gm. of zinc furnish 96,540 coulombs.

We must therefore furnish ^^ ^,^ x 32.7 gm. of

96,540 ^

zinc per second; 0.118 gm. of zinc per second or
426 gm. per hour will give 0.5 H.P.

If we set up a whole row of Daniell cells as a
battery, and draw our 0.6 H.P. from this, we will be
much nearer the practical truth, for it would take
an enormous cell to give 360 amperes, owing to the

STORAGE BATTERIES

rather high intermil resistance caused by the porous

cup.

19. Cells in Series and Parallel. — Suppose we have
100 cells in our battery, each with an electromotive

FiQ. 5. — Cells connected in parallel. The effect is the same as though
all the plates were placed in one large cell.

force of 1.1 volts. If they are connected so that the
zinc of eacli cell is fastened to the copper of the next

Fio. 6. — Cells connected in scries.

one as shown in Figure 6, their electromotive forces
will add, and our whole battery will have an electro-
motive force of 110 volts. To get 373 watts or 0.5
H.P. we need to draw only |J J = 3.4 amperes from

SOME ELECTROCHEMICAL FUNDAMENTALS 29

our battery, and this would not be an unreasonable
current for large Daniell cells. You will notice that
the total weight of zinc dissolved and copper de-
posited is exactly the same ^s though it had taken
place in one huge cell, though now it is distributed
over 100 cells.

In our very first problem, on page 17, where we
calculated the current required to deposit a ton of
copper per hour by electrolysis, we obtained a value
for a single huge cell. Practically copper would
never be purified in that way, -for the voltage nec-
essary to deposit copper is not more than 0.3 volt,
and it is not feasible to build a generator to work at
that voltage. Besides, it is not necessary, as it is just
as well to work a number of electrolytic cells in
series like a battery. In many copper refineries 200
such cells are used and a current of perhaps 4000
amperes is sent through the whole series. This re-
quires a generator capable of giving this number of
amperes at about 60 volts, and the power required is
therefore 240 KW. The copper deposited has the
same weight as though 800,000 amperes were sent
through a single cell, and is therefore a little over a
ton per hour.

CHAPTER III

ABOUT IONS

20i All electrochemical processes follow Faraday's
law absolutely as far as any one can find out, and
they therefore invariably depend on ions in the sim-
ple sense in which Faraday himself used this term
(page 12). There is, nowadays, a whole field of
science which has to do with the study of the ions
of gases, and some of the most interesting and sug-
gestive of all modern developments are being made
in this field. These hypotheses and theories, now
just being cleared of their mysteries and made a
part of general science, will ho doubt some day be-
come a safe and useful basis for the study of electro-
chemistry. But for the present, at least, we will be
safer if we stick close to Faraday, and call our ions
*' . . . those bodies which can pass to the electrodes."
We shall meet with rather strange ones when we
come to the lead storage cell itself, and some general
knowledge of the simpler sorts will be found a useful
introduction.

21. Condaotanoe by Ions. — In the first place, the
ions are already there in a solution of a metallic salt

ABOUT ION 8 31

or in a molten electrolyte. They are not produced
by the action of the current. And they are able to
begin carrying electricity toward the electrodes as
soon as the circuit is closed. It is also certain that
they do all the work of carrying the current through
the cell. These last two statements are merely an-
other way of stating the extreme accuracy of Fara-
day's law. No current seems to pass through an
electrolyte unaccompanied by the movement of an
exactly equivalent amount of each of two ions —
an anion and a cation.

Water itself is a conductor of the electrolytic kind.
It has a high resistance, to be sure, but it does con-
tain small concentration of the ions H"^ and OH".
It is chiefly remarkable for the aid it gives to other
substances in the process of ionization. Metallic
salts, and acids and bases as well, are famous carriers
of current when they are in solution in water, and
they always follow Faraday's law. Many of them
are also good conductors in the molten state, and
their ions pass to the electrodes under these circum-
stances just as well as they do in water.

22. Chemical Facts conneoted with Ions. — Since
Faraday offered his suggestion about the names to
be used in describing the process of electrolysis, and
gave to the ions their simple definition, much of
chemistry has been restated. The general facts
about solutions, and especially those which have to

82 STORAGE BATTERIES

do with ions, even apart from their power of carry-
ing a current, have been brought together into one
of the most united and easy branches of the science
of chemistry. Let us consider a few of the simpler
generalizations. All acids in water solution contain
hydrogen ion, H+, and their acid properties are de-
pendent on its presence and are measured by its
concentration. All bases in solution contain 0H~
(hydroxyl ion). Solutions of metallic salts usually
contain an ion produced from the metal, like Cu"*'^,
Zn++, Ag+, K+, Al"^"^+. Pb^"*", and an ion formed from
the other part of the salt — CI", Br", NOg", ClO^",
SO4 — , CrO^ — . We quickly get into the habit of
thinking about the particular ion we want for any
special set of properties it may have, and I have
often heard a student just beginning chemistry —
one who had not the slightest idea of Faraday's law
or of any electrochemical theory — say to his neigh-
bor, " Pass the copper bottle," when he meant copper
sulphate or nitrate or any other soluble copper salt.
He needed copper ion for his experiment, and in
the same way a more advanced student will ask,
"Have you some acid?" when he wants hydrogen
ion. In neither of these cases does the other ion,
which is sure to be present, interest the chemist, pro-
vided it has not some special peculiarity of its own.
But if the other ion can form a difficultly soluble salt
with one of those in his test tube, he will be more ex-

ABOUT I0N8 33

plicit in stating the kind of copper salt solution or the
kind of acid solution he needs. If you will think over
your own experiences with solutions of acids, bases,
and metallic salts, you will see that the chemistry of
aqueous solutions can all be brought into the easiest
form by a classification of the properties of ions.
Besides this, one only needs knowledge of the solu-
bilities of salts to have a pretty full command of the
facts about aqueous solutions.

This same statement is almost equally true of
electrochemistry. A current only passes through
a solution when two ions carry it. These ions pass
back and forth at the electrodes and send their quota
of electricity out through the wires of the circuit as
a current. Each ion travels through the electrolyte
with its own special velocity and carries a fraction
of all the current flowing which is proportional to
this velocity. If we had space for a really complete
theory of galvanic cells, we would need careful study
of the changes which take place at various parts of
such a cell as the result of differences in ionic migra-
tion velocity. We should at the same time find
some very simple and interesting generalizations
about the part played by the individual ions in elec-
trolytic conductivity.

23. The Ionic Theory. — In some of our explanations
we shall feel the need of a much more minute and
detailed picture of what happens than can be bb-

34 STORAGE BATTERIES

tained by adhering closely to Faraday^s careful defi-
nition of an ion. We shall need to bring in occa-
sionally a more hypothetical, or rather theoretical,
ion than Faraday's. This does no harm, for more
and more proof of the general usefulness and trutii
of the general theory of ions is being accumulated
every day. The step from Faraday to the theoretical
picture is not a great one.

Ions are, in this picture, parts of molecules, each
one connected with a definite and constant quantity
of electricity, either positive or negative. If we
collect enough of these little carriers to make a
gram-equivalent, and send them along to discharge
against an electrode, 96,540 coulombs will pass this
surface and flow out through the wires of the exter-
nal circuit. At the same time enough of the ions of
opposite sign to carry the same quantity of electric-
ity will have been discharged at the other electrode.
Faraday's ion was singular, and we shall refer to an
ion as it when we need no further statement than
that involved in Faraday's law. When we want to
describe the more complicated changes about the
electrodes, we shall make use of the other picture and
refer to the ions of copper or silver, using the plural
and picturing an electrolyte filled with them, each
carrying its unit quantity of electricity, and all
swarming toward the electrodes when current passes.

The electrolyte which is used in a storage cell is

ABOUT IONS 35

a rather concentrated solution of sulphuric acid in
water. It contains considerable concentrations of the
ions H'*' and SO4 , and these do the carrying of the
current across the space between the electrodes.
During the passage of current in either direction, H'*',
the cation, moves toward the cathode, whichever
plate this may happen to be, and at the same time
SO4 , the anion, moves toward the anode. The
direction of flow of the current is reversed when the
cell passes from charge to discharge and the direction
of the motion of the ions changes also.

24. Mig^tion Velocities. — If both the ions moved
through the electrolyte with the same velocity, there
would never be any difference in ionic concentrations
in any part of the cell. It was found a long time ago
that considerable differences are set up during elec-
trolysis, and from measurements of these concentration
differences it was found possible to calculate the
relative migration velocities of all the ions. Later
the actual velocity with which an ion passed through
the solution was measured, and, of course, as soon
as the real velocity of motion of one single ion was
found, all the other velocities could be calculated from
the relative numbers found by means of the concen-
tration differences.

H"*" ion moves through the solution about five times
as fast as SO4 . Figures 7 and 8 show the condition
of things in the cell (7) before any current has

36 STORAGE BATTERIES

passed, and (8) after 6 SO4 ions have separated at
the anode.

We must remember that the number of + and —
ions must always be the same at any point in the cell.

ooooooooboooojoooooooo

I I

ooooooooooooooooioooooooooooooooooooooooooo

I I

Fig. 7. — Diagram of ion concentrations in an electrolytic before cur-
rent begins to flow.

The attraction of the -h and — charges on these very
small bodies is so great that we can never hope to get
more than the most minute concentration of any one
kind of ion off by itself, and we have very good evi-
dence that our solutions are everywhere electrically

00
00

000 poooopoooooo^^

I I 000

I I CX50

000000 1000000000000000000000000000

I I

000

Fig. 8. — The cell of Figure 7 after six SOi — ions have left the electro-
lyte at the anode.

neutral, which means that the concentration of + and
— ions is everywhere the same.

This statement suggests the question : How can a
slow-moving ion get to its electrode fast enough to
keep up the supply there ?

And the answer is that it cannot keep the concen-
tration at its original value. During electrolysis the

ABOUT IONS 37

electrolyte about the place where the slow-moving
ion is going out of solution is depleted. Its concen-
tration becomes less and less, until diffusion finally
stops the dilution. In the meantime the fast-moving
ion has become heaped up about its electrode. The
diagrams in Figures 7 and 8 will make this clear.

When the current begins to flow, the H"*" ions move
toward the right, and are removed at the cathode
(either as gas or by some secondary reaction), and at
the same time the SO4'" ions move toward the left,
and are removed at the anode. The H"^ ion moves
five times as fast as the SO4 ion. By the time six
SO4 ions have passed through the electrode, 12
hydrogen ions have gone out of solution. 10 H"*"
ions have in this period of time entered the region
about the cathode, and one 804"" ion has entered the
region about the anode. The region in the center of
the cell has not changed in concentration, but the
parts of the cell on both sides of it have changed,
and the relative change has been a large one.

It will be seen at once that the relative migration
velocities are inversely as the losses abont the electrodes.
The cathode has lost one, the anode has lost five, and
the migration velocities are as five (cation) to one
(anion). This means, too, that five sixths of all the
electricity that has passed through the cell has been
carried through by the cation, and only one sixth by
the anion.

STORAGE BATTBBIB8

25. lonio BMction. — In cells of the Daniell type
the ionic changes are very simple. A single cation
carries the current toward the cathode* and leaves
the electrolyte at that electrodt, while a single anioD
attends to all the cell activities at the anode. The
concentration changes which result fi'om talcing away
material from the electrolyte at the cathode and
from adding it at the anode are indicated in Figure 9.
In our storage
ipp£R ^^'^ ^^ have a
much more com-
plicated system.
H+ and SO,--
do not pass in
and out at the
electrodes, and
siuihvDamcii the really fun-
damental cell
activities are cared for by other ions. The ions
which are active at the electrodes do not travel a
measurable distance into tlie main body of the elec-
trolyte. We must therefore expect two sets of ionic
reactions in a storage cell — those between the con-
ducting ions and the active electrode ions and those
between the lictive ions and the substances of the
electrodes. We shall examine some possible and
plausible theories in Chapter VIII.

— CoucpntratEonchai]

CHAPTER IV

THE FUNDAMENTAL CELL REACTION

26. An active storage cell contains two quite
different kinds of plates immersed in a rather strong
solution of sulphuric acid. In storage battery par-
lance one* of the plates is called the " negative " and
the other the "positive." In spite of the fact that
the cell reaction is completely reversed each time the
cell is charged and discharged, so that each plate is
really positive half the time and negative the other
half, these terms are about as good as any that can
be found. Anode and cathode are no more definite.
Lead plate and peroxide plate could very well be
used, and by " the positive plate " is meant the one
which has lead peroxide as its chief constituent.
The "negative" is the one which has as its chief
constituent spongy, finely divided metallic lead.

In order to apply the laws which we have developed
for galvanic cells in general to the case of the lead
accumulator we must first of all know exactly what
chemical reaction takes place when current flows
through the cell.

40 STORAGE BATTERIES

27. The Lead Cell Keaction. — The complete re-
action of a lead accumulator, working under ordinary
conditions of service, is

Pb + PbOa + 2 HjSO^ <^ 2 PbSO^ + 2 U^O,

and the sign ^ indicates that it is perfectly revers-
ible. During discharge the reaction goes from left
to right. It takes place of its own accord and the
cell furnishes electrical energy which can be utilized
for work outside the cell. Under these circumstances
the sponge lead plate is the anode, — lead goes into
solution as lead ion, Pb"*""*", here, — and the peroxide
plate is the cathode — lead peroxide is reduced to
lead ion there. Everywhere in the cell the lead ion
which is produced finds SO4 handy, and since lead
sulphate is a difficultly soluble substance, the two
ions unite to form non-ionic lead sulphate, which soon
saturates the solution and precipitates in solid form.

28. Effect of High Current Bensity. — It has been
said that the reaction is completely reversible as long
as the currents sent through the cell are anywhere
near the limits of practical operation. If a very
large current is sent through a cell with very small
electrodes, secondary effects appear in measurable
amount. Persulphates are formed and some other
complex ions make their appearance.

Ordinary Cnrrents. — In ordinary practice all these
effects can be wholly neglected. If we are working

TBE FUNDAMENTAL CELL REACTION 41

with a comparatively large cell, we can take out the
electrochemical unit of quantity of electricity with-
out greatly changing the distribution of materials in
the cell, and by the time 96,540 coulombs have been
sent through, ^^ gm. of lead have been changed
to lead ion at the anode (the lead plate) and ^|A
gm. of lead peroxide have become lead ion at the
cathode (the peroxide plate). At each plate these
amounts of lead ion have found sulphate ion waiting
for them and equivalent amounts of lead sulphate
have been precipitated — ^|^ gm. at each plate.
Nothing has yet been said about the nature of the
ion which travels back and forth at the peroxide
plate. Whatever this ion may be, it is evident that
its decomposition into Pb^"*^ leaves 2 behind, and
from the reaction it can be seen that the sulphuric
acid which reacts with the lead ions furnishes enough
hydrogen to produce 2 HjO at' the positive plate.

29. Reaction during Charge. — If now we charge
the cell, after a period of discharge, we merely re-
verse everything that happens during discharge.
The peroxide plate is now the anode. Here lead
ion goes out of solution — leaves the ionic state — and
with the aid of the water in the electrolyte becomes
lead peroxide. At the lead plate, which is now the
cathode, lead ion changes into metallic lead, just as
at any other simple metal-ion electrode. At both
plates it is the lead sulphate which furnishes the

42 STORAGE BATTERIES

constantly renewed supply of lead ion for the reaction.
This seems a little difficult at first glance, for is not
lead sulphate an insoluble substance ? If it were
really insoluble, of course our cell could not work in
this way, but it is not. It has a perfectly definite
and well-known solubility, and while the concentra-
tion of lead ion in the solution is very small indeed,
it must be remembered that the reservoir of lead sul-
phate is very near at hand, so that the supply of lead
ion has only " molecular " distances to travel to the
point where it is to be used.

30. Proof of the Formula. — This fundamental re-
action has been tested with the greatest care by many
investigators. There are evidently several things
to be proven and there are several ways of proving
some of them.

What we must know is this. When we pass 96,640
coulombs through the cell in tlie discharging direction,
is the result the formation of ^^ gm. of lead sul-
phate and ^^ gm. of water? During this same
period has the lead plate lost ^^ gm. of metallic
lead and has the peroxide plate lost ^|^ gm. of lead
peroxide? And during the same period has the
electrolyte decreased its acid content by ^^ gm.
of H2SO4?

These points must be proven for the discharge re-
action. We must also prove that the reaction is per-
fectly reversible and that during charge exactly the

TBB FVSDAMESTAL CELL BSACTION

sune amounts of exactly the same materials react,
and no otHen, the reaction being now from right
to left.

The change in the content of lead, lead peroxide,
and lead sulphate in the plates must he JEouad by

--^

careful chemical analysis of plates after various times
of charge and discharge.

Figure 10 shows the results obtained by analyzing
the active material of the positive plate after various
times of charge and discharge. It will be seen that
the content of the plate in peroxide is accurately pro-
portional to the amount of electricity which has
passed through the cell, just as required by our fun-

STORAOS BATTERIES

damental reaction. Similar analyses of the active
material of the negative plate show similar curves
for the lead content, and the lead sulphate content has
been found to be an equally good indication of the
condition of the cell as to charge or discharge.

The easiest of
all the changes
to follow is that
in the electrolyte.
Here we can fol-
low the change of
concentration by
merely measur-
ing the density
of the acid from

This is shown in
Figure 11. Evi-
dently there will
be a lag of density behind the value properly belong-
ing to any given time after charge or discharge has
begun. For the acid is being formed or used up in-
side the plate, and must diffuse in or out as the re-
action goes on. Tliia is a comparatively slow process,
and we must therefore expect that just at the begin-
ning of either charge or discharge the acid density
will remain constant, even though some current has
passed. The curves of Figure 12 are for the very

£u)

Tax FUNBAMENTAL CELL REACTION 45

beginning of charge and discharge, and they show
this lag effect very clearly. These are reallj' pieces
which belong at the beginning of the curves of Figure
11, but they would not show if plotted in the time
units of that figure. In their own
diagram the time axis is greatly
drawn out to show the effect more
clearly.

When we have once decided that
this fundamental reaction really
represents what happens in a lead
accumulator during its practical
operation, we have made a great
step, and with the aid of the gen-
eral theory developed in earlier
chapters we can go a long way
toward explaining the effect of va- Fio. 12. — First part
rious factors on the cell. E^a'I^^Bcalf ^ '

It has taken a long time to gather
the evidence which proves the correctness of our fun-
damental cell reaction, and there are probably a good
many storage battery experts who still feel doubtful
as to its comp1et«ness. Many of them have wished
to introduce intermediate steps, such as the forma-
tion of lead persulphate or persulphuric acid at the
peroxide plate during charge. It is evident that as
long as the processes assumed are reversible and lead
to the same final formula as the one we are using, any

STORAGE BATTERISa

number of intermediate reactions could be assumed
without affecting the validity of our reaction in the
least. But even this opportunity for introducing
hypotheses and analogies is removed when we ex-
amine the electromotive force equations for the cell,
which we shall take up in a future chapter. When
all the evidence is taken into consideration, our fun-
damental reaction seems to be proven.

CHAPTER V

THE ACTIVS IONS

31. It does not take any tndtiing in theoretical
science to make it quite clear that the actual carry-
ing of current through the storage cell is done by
the sulphuric acid, and we can be very sure that it is
done by the ions H"*" and SO^"". Both lead and
lead peroxide are so very slightly soluble in sulphuric
acid that their presence in the electrolyte can hardly
be shown by analytical means. The concentration
of the ions which pass back and forth at the elec-
trodes must always be exceedingly minute, and this
small amount of ion cannot have the least relation
to the huge current that can be sent through a large
storage cell.

In this respect the storage cell differs from most
galvanic cells. And it is precisely in this very point
that the remarkable properties of the lead cell as
an accumulator are all bound up. If the ion of the
electrodes reached any large concentration, we would
have all the difficulties in the way of trees and short
circuits which appear in most cells when we try to
reverse them and use them as accumulators. The

48 8T0BA0E BATTERIES

active material would soften and move all about the
cell, growing at the favored points and not at the
others. In the lead cell material produced during
either charge or discharge is deposited " right in its
tracks," to use a homely expression, and the plates
preserve their condition.

32. What Ions carry CiuTent? — But if the current
is all carried by ions which do not pass back and
forth at the electrodes, there must somewhere in the
cell be a loading and unloading of electricity from
ion to ion, and the complete expression for the cell
reaction should show this transfer. As a matter of
fact it cannot be shown by any purely chemical
means, nor is it at all necessary to try. The reaction
we have adopted is the necessary and complete ex-
pression for everything that takes place in the cell,
from a merely chemical point of view. We can get
some theories which fit the facts pretty well, and
it will be seen a little later that these theories are
subject to rather severe tests of a quantitative sort.
At any rate, it is always interesting to develop the
possible theories for such a chemically unattackable
problem, and so we will examine one of the most
plausible.

33. At the ITegative Plate. — Let us start with the
negative plate. During discharge this is the anode
of the cell. The acid is doing the carrying of current
through the cell, and SO^ ion is therefore moving

THE ACTIVE I0N8

toward the anode. The electrode is probably re-
versible with respect to Pb"^"*" ion, and lead goes into
solution as Pb''"'" in proportion to the amount of cur-
rent which passes through the electrode. It never
gets far, for the SO^"" is moving toward it, even if
there were not enough in the electrolyte, and lead
sulphate is precipitated in the very spot where the
lead ion was formed from the metal. The only
thing that is left over after this reaction has been
completed is hydrogen ion, H"*", and this is doing the
carrying of current through the electrolyte toward
the cathode, — in this case the peroxide plate. If
we can take this extra H"^ into our reaction at the
cathode, we will be able to reach a balance, and our
theory will at least be a possible one.

Leaving aside for the moment the matter of the
ions, we can say with certainty : —

Sulphuric acid carries the current across the space
from plate to plate. The acid is separated during
this time into 2 H and SO^.

For discharge

Pb + SO^
PbOa + Ha-hH^SO^

In sum

Pb -h PbOj + 2 HaSO^

34. At the Peroxide Plate. — It does not require a
very vivid scientific imagination to discover a simple

PbSO^.

PbSO^ + 2 HaO.

2 PbSO^ -h 2 HjO.

60 STORAGE BATTERIES

and reversible reaction which takes in the ionic
change at the lead plate.

Pb ^ Pb++.

Metal

Pb++ + SO4- -)^ PbSO..

8oUd

For the peroxide plate we need a more complicated
set of changes, and Liebenow has suggested an ion
which fits the facts very well indeed. Suppose the
peroxide plate to be reversible with respect to the
PbOj"" ion. We then have at this plate during
discharge

PbO„

PbO»~,

8oll<l

PbOj-

-+4H+

Pb+^- + 2 H,0,

Pb++

+ SO,"

PbSO.,

Solid

and if we add the reactions at the lead and lead
peroxide plates, we get

Pb + PbO« + 2 SO4— + 4 H+ ^ 2 PbSO. + 2 H«0,

Metal Solid Solid

which is our fundamental reaction

Pb + PbOa + 2 HaSO^ ^ 2 PbSO^ + 2 HjO.

This is completely reversible, and it will also be
found that our separate ionic reactions represent
completely reversible changes.

35. Diagrams of Charge and Discharge. — The accom-
panying diagrams may make all this still clearer.
The cell is discharging — it is furnishing current

THE ACTIVE I0N8 51

for use in the external circuit. The current is flow-
ing into the cell at the lead plate, which is therefore
the anode. Here metallic lead passes through the
electrode (Fig. 13) and changes into lead ion, Pb"*"*",
carrying 96,540 coulombs with it for each ^^ gm. of
lead that go into solution. The lead ion has hardly
passed the electrode before it meets with SO4 in
the electrolyte (Fig. 14). Lead sulphate being so
slightly soluble, it requires only a very small concen-
tration of lead ion and sulphate ion in solution to
reach the limit of solubility of lead sulphate. This
substance is therefore formed from the two ions as a
solid, and removed from .the electrolyte as fast as it
is produced.

36. Discharge. — On discharge (see Figure 14) the
lead peroxide plate is the cathode. It is certainly
reversible with respect to some ion, and PbOj seems
to fit the necessary conditions. This PbOj is con-
stantly formed from the solid PbOj of the plate, just
as Pb"'"''' is formed from the solid lead of the anode.
It starts toward the anode, being an anion, as its
two — signs indicate. Before it has more than
passed the electrode it meets with H+, of which
there is always plenty about in a concentrated sul-
phuric solution, even if it were not moving toward
the cathode carrying the current. It reacts with
this H+, forming Pb"^"*" and water (Fig. 15), and the
Pb"'"''", finding SO4 in plenty, soon saturates the

®®®®

-.@®-

ftS<^.

Fio. 15. — Thclhird

stage in the dis-
chorse reaction.

\ Tl Q

PlS(^

►^0

Fia. 16. — DiachargG a

THE ACTIVE IONS 53

solution with lead sulphate, which is precipitated
very nearly in the spot from which the peroxide
started (Fig. 16).

It will do no harm to go over the changes in the
reverse direction, just to fix the whole reaction more
firmly in our minds.

Charge. — The cell is charging (see Figure 17) . The
peroxide plate is now the anode, and contains a con-
siderable proportion of finely divided lead sulphate
from the previous discharge. Pb"*""*" and SO^ are
formed as fast as they are needed from this reser-
voir in the plate, and the Pb"*"*" reacts with the water
of the electrolyte, forming H+ and PbO^ (Fig.
18). The PbOj passes through the electrode (Fig.
19) and is deposited as solid PbOj very close to the
point where lead sulphate went into solution. H"*" and
SO4 are left in the electrolyte in proportion to the
amount of current which has passed (Fig. 20).

The lead plate is cathode during charge. Here
also there is a reservoir of fine lead sulphate from
the previous discharge. This furnishes a constant
supply of Pb"^"*" and SO4 , and the electrode is re-
versible with respect to Pb"^"*". So Pb"*"*" passes out
and changes to metallic lead, sending a correspond-
ing quantity of electricity along through the ex-
ternal circuit, while the SO4 finds itself moving
toward the anode. It will find its equivalent of
H+ in the solution, and our equations show that

jpisiv

pisa.'Sffi

Is;

Fio. 17. — The begiiming of charge. Fio. 18. — SeooDd stage of the charge re-

action.

-J ! 1

Si N

Pi.(li

Fio. 19. — Third stage in charge reaction.

FiQ. 20. — Charge complete.

TUE ACTIVE ION 8

acid is produced during charge in proportion to the
amount of material reacting, and that it is used up
in the same proportion during discharge. It also
expresses everything else that is contained in our
fundamental reaction, and gives us at least a pos-
sible picture of what takes place at the electrodes
as well. We have shown that it is quite possible
to have all the current carried through the cell from
plate to plate by the ions of the acid, provided these
two ions react near the electrodes to produce ions
like the ones we have assumed. Our electrode
reactions are perfectly reasonable ones, and are, as
matter of fact, supported by a great deal more evi-
dence than we can yet call to their support. We
shall return to them in a later chapter.

CHAPTER VI

SOME PERTINENT PHYSICAL QUERIES

37. A host of questions arises even at this early
point in the discussion of the lead storage cell.
Even if we suppose that we have satisfactorily dis-
posed of the chemical changes, and found a pair of
ions that might do the work at the electrodes, how
can we explain a good many things about the pe-
culiar nature of the materials of the cell ?

Premises. — These questions can best be discussed
if the reader will keep in mind : —

(I) The ions which pass back and forth at the
electrodes have only molecular distances to travel.

(II) The particles of active material are very
small indeed.

(Ill) The active materials: — lead, lead peroxide,
and lead sulphate are all very slightly soluble in con-
centrated sulphuric acid.

38. Queries and their Answers. — Query 1. How
can storage plates keep their shape? How does it
happen that a battery can be sent through thousands
of charges and discharges without much growth of
trees or sponge ?

SOME PERTINENT PHYSICAL QUERIES 57

Just because all the solid substances concerned
are so very slightly soluble in the electrolyte. The
ion which passes back and forth at the electrode has
no chance to wander far enough to deposit at even
a measurable distance from its point of origin.
SO4 is everywhere waiting for the Pb''"'", and in-
soluble PbSO^ is precipitated almost instantly. This
is one of the prime secrets of the success of the lead
cell, and the main reason why its plates preserve
their mechanical structure as well as they do. In
another sense it is a disadvantage, for it means that
the particles of active material will be exceeding fine
and small, and that there will not be much inter-
growth and interlocking between neighboring par-
ticles. In the ideal cell both extreme insolubility
and intergrowth of particles might occur simul-
taneously, but not in practice.

Query 2. The lead peroxide of the positive plate
is in contact with a lead support. Why does not
the plate discharge of its own accord ? Does it not
contain all the necessary substances for the reaction

Pb + PbOa + 2 HaSO^ ^ 2 PbSO^ -h 2 H2O ?

It does; and self -discharge always takes place
when a peroxide plate is standing fully charged.
But before it has gone far all the finely divided
rough lead on the surface of the lead support has
reacted and then the plate is protected by its dense

68 STORAGE BATTERIES

layer of lead sulphate, just as a lead plate protects
itself in sulphuric acid.

If the surface of the lead support is roughened or
increased, the action will be stronger, and Plants
plates were originally formed for service by means
of this very action. Our modern plates have a very
much greater proportion of active material to surface
of lead support, and therefore the loss of energy due
to this ^^ local action " is a comparatively small one.
(See page 182.)

Query 3. How does it happen that a lead accu-
mulator with a difference of potential of two volts
between its plates can stand on open circuit without
immediately discharging itself? Under proper con-
ditions water (made acid with sulphuric acid) can
be completely decomposed into hydrogen and oxy-
gen at 1.5 or 1.6 volts. Why does not our cell
begin to decompose its electrolyte and keep on form-
ing gas until the plates are quite discharged ?

Because the plates of our cell are made of lead and
lead peroxide. There is a great difference in the
amount of work required to form bubbles of hydro-
gen rapidly on surfaces of various metals. It takes
2.5 or 2.6 volts to cause gas to form rapidly in a
lead accumulator, and at 1.6 volts — the electromo-
tive force at which gas forms on platinum electrodes
— hydrogen forms bubbles so slowly on a lead sur-
face that losses due to this cause are quite negligible.

SOME PERTINENT PHYSICAL QUERIES 69

Even at 2 volts the evolution of hydrogen is so slow
as to be unmeasurable. (See page 217 for the effect
of impurities.)

Query 4. How can it be that lead sulphate is
formed during the discharge of our cell, and how
can this substance change back so readily to lead
and lead peroxide? Is not ** sulphation " the most
dangerous disease that can come upon a battery ?

The explanation is a matter of surface, like so many
others in this subject. The lead sulphate which
forms in the plate during a healthy discharge
differs greatly in size of grain from the same sub-
stance taken from the bottle on the laboratory shelf,
and just as much from the material which causes what
is called in battery parlance "sulphation." If ordi-
nary commercial lead sulphate be made into a paste
and filled into a lead support, it does not change to
lead at the cathode and lead peroxide at the anode
easily. It can be subjected to the action of the cur-
rent for a very long time without being completely
transformed, and it never does make a good coherent
plate. When a cell is allowed to stand discharged
for many weeks the fine grains of sulphate which
are formed during normal discharge suffer an inter-
esting change. True crystallization begins on the
larger particles, and the substance goes into solution
at the small ones. It moves through the solution
and continues to deposit on the large grains until

60 STORAGE BATTERIES

the small grains have completely dissolved and the
large ones, fewer in number, have grown to consider-
able size. The plate is now sulphated, and if it is
charged for the ordinary time, it by no means returns
to its original condition of healthy charge. The large
crystals of sulphate do not go into solution com-
pletely. In fact, they hardly dissolve at all, and
long before the cell has been brought back to its
charged state reaction has ceased and the current is
merely producing gas. It is possible to restore a
sulphated cell, but the charge must be continued so
long that gassing breaks up the active material, and
even when the remaining sulphate has all been forced
to react, a large part of the original capacity of the
cell has been lost. (See page 216.)

Query 5. Metallic lead in the form of a bar or
plate is not dissolved by sulphuric acid under ordi-
nary circumstances, and this is especially true of acid
of the concentration used in storage batteries. The
grids of paste plates and the main body of Plante
plates resist the attack of the acid during the whole
life of the plates. Lead is one of the metals which
"protects itself" from solution in reagents by the
formation of a dense layer of slightly soluble material
on the surface. It is a familiar fact that lead pipes
cannot be used for pure distilled water without
danger of contamination, for in this case the sub-
stance formed is not dense and does not protect the

SOME PERTINENT PHYSICAL QUERIES 61

metal. The hydroxide which forms under these cir-
cumstances is fluffy and breaks away from the sur-
face, and the plate rapidly dissolves. But if the
water passing through the pipe is not pure, — if it
contains carbonates, chlorides, and sulphates even in
small amounts, — dense protecting coatings of carbon-
iate, chloride, or sulphate are formed and the metal
is no longer dissolved. It is safe enough to use lead
pipes for ordinary water even if it is to be used for
drinking purposes.

How is it, then, that the lead of the negative plate
can pass easily and rapidly into the form of lead
ion? Why do not the particles of lead so protect
themselves and refuse to react? And if because of
their very fineness the protecting layer which might
be formed makes up a considerable part of the whole
bulk of the grains, why does not the self-discharge
necessary to produce this protecting layer greatly
reduce the activity of the lead plate?

While it is quite true that the particles of lead on
the negative plate are very small, they are still quite
large in comparison with the protecting layer of sul-
phate which is sufficient to prevent further action.
At the end of charge a part of the energy is lost by
formation of sulphate at the lead plate, but in prac-
tice it is a very small fraction of the whole. But
when current is passing through the cell in the dis-
charge direction a very different state of things pre-

8T0BAQE BATTERIES

vails. Suppose our cell to be first on open circuit
and that we are looking at what happens at the lead
plate and able to see everything that occurs. Lead

changes to lead ion,

Pb''""*', and this goes

into solution, leaving

the plate negatively.

charged. The Pb++

finds SO4 waiting

m and precipitates as in-

^ soluble PbS04, but it

^ leaves 2H''" behind it,

P^ and the condition of

strain set up by the

positively charged ion

in the electrolyte and

the negatively charged

plate is not relieved

(Figure 21). It only

takes the presence of

a very small concen-

Fio. 21. — ElcctiOBtatio equilibrium tration of ion in solu-
about a lead plate. .. „ ,^ ^. „^ ^„ „^

tion to set up an at-
traction so strong that no more ion leaves the plate.
The electrode is in equilibrinm with respect to Pb"^"*".
It has protected itself sufficiently by sacrificing a very
minute fraction of its whole mass.

But as soon as the external circuit is closed and

SOME PERTINENT PHYSICAL QUERIES 63

current begins to pass, the H"*" is no longer bound by
an electrostatic attraction. The lead plate can dis-
charge itself through the wires and the H"*" can pro-
ceed on its way toward the cathode, carrying its
equivalent of electricity with it. The electrode is
no longer in equilibrium, and more lead goes into
solution, becomes Pb''"'", reacts with SO4 , and frees
more H**". This continues as long as current is
being taken from the cell.

CHAPTER VII

SNSRGT RELATIONS

39. Any arrangement whatever which runs of its
own accord and which can furnish energy for doing
outside work as well must draw upon some store for
the energy expended. A charged storage cell con-
tains potential chemical energy. It differs in no way
from any other galvanic cell in this, and if we knew
of practical ways of manufacturing lead sponge and
lead peroxide of exactly the same physical character-
istics as those possessed by the active materials of
our charged accumulator, we could build a cell just
like it in every way without any charging process
whatever. It merely happens that the very best
way of manufacturing lead sponge and lead peroxide
of exactly the right quality is to pass a current of
electricity through a discharged storage cell. The
materials themselves are no more electrical than the
same substances in bottles on the laboratory shelf.

40. Transformations of Energy. — There is hardly a
branch of science where we can be so sure of our
footing as in calculations which involve the trans-
formation of quantities of energy from one form to

ENERGY RELATIONS 65

another, especially in the calculation of reversible
changes, and it is difficult to imagine any arrange-
ment which could be more perfectly reversible than a
storage cell. Small losses occur even in a big storage
cell. Some gas escapes and cannot be taken into
our calculation, and there is some local action at the
plates with corresponding evolution of a little heat.
But the same is true in any arrangement known to
man, and in most cases the losses are very much
greater than in our cell.

Eleotroohemioal Beaotion. — We can apply the law
of the Conservation of Energy. Applied to our
own particular case this law says : If we have at our
disposal a system, represented by

Pb + PbOa + 2 HaSO^

and consisting of 207 gm. of lead, 239 gm. of lead
peroxide, and 196 gm. of sulphuric acid, and this
system changes of its own accord into another

2 PbSO^ + 2 HjO

consisting of 606 gm. of lead sulphate and 36 gm. of
water, a definite and determined amount of energy
will be set free, which can be utilized for doing
work. If the reaction is perfectly reversible and no
energy has managed to get away from us, we can
restore the original condition of the system by ex-
pending the same quantity of energy on it.

66 STORAGE BATTERIES

Our own special interest lies in a chemical reaction,
but the same law applies for any cliange whatever.
The original condition might be represented by a
certain mass of water at the top of a dam and the
final condition by the same mass at the bottom.
Here we would have no difficulty in calculating the
quantity of work obtainable by the fall of tlie water,
and the same amount of work would carry it back
to the top, provided all our machines were friction-
less and worked with 100 % efficiency.

4L Thermoohemioal Reaction. — Now for the next
step. If we should take the amounts of the various
materials on the left side of our fundamental equa-
tion, and should mix them all up into a pasty mass,
we would not get any electrical current from it, but
we would get a definite amount of heat set free.
We will get the same total amount of energy from
the reaction in either case, provided our cell does
not itself heat up or cool down during the reaction
of these amounts of its materials. In the one case
we should measure the amount of available energy
in heat units, or calories, and a calorie is the amount
of heat required to raise the temperature of 1 gm. of
water 1® C. In the other case we should measure
the amount of available energy in electrical units,
joules (volt-coulombs).

42. Heat Changes in the Cell. — If our cell does heat
up while it is sending out its 96,540 coulombs, we

ENERGY RELATIONS 67

must remember the amount of heat which appears in
this way, and we must expect to get less energy
from the cell for use in the external circuit if a part
of the total energy of the reaction has been used to
heat the air of the room. If the cell cools while it
is working, we might expect to get more than the
calculated amount of energy, and to this point we
will come back later.

But if the cell neither heats nor cools during the
passage of 96,540 coulombs, the law of the Conser-
vation of Energy gives us our

First Fundamental Equation

ohemical energy expanded = electrical energy produced.

Before we can go any farther we must know the
numerical factor for transforming joules to calories
(or vice versd)^ and this has been often determined.
It takes 4.18 joules to raise the temperature of 1 gm.
of water 1° C.

The determination of the heat of the reaction

Pb + PbOa + 2 HjS04;it2 PbSO^ + 2 Ujd

cannot be carried out directly with accuracy because
of the slowness of the reaction when the substances
are mixed up together. It can only be determined
by indirect measurement, and the best results have
been obtained by using very dilute sulphuric acid.

Applying a correction to be explained immediately,
the heat of this reaction for acid of density 1.044

68 STORAGE BATTERIES

(0.70 gm.-mol. HjSO^ per liter of electrolyte) is
87,000 calories. A cell containing acid of this den-
sity neither heats nor cools while it is working.
Now see how simple our calculation becomes :

87,000 calories x 4.18 = 364,000 joules,

and this is the amount of electrical energy which be-
comes available when 207 gm. of lead and 239 gm.
of lead peroxide have reacted with 196 gm. of sul-
phuric acid (in rather dilute solution) to produce
606 gm. of lead sulphate and 36 gm. of water.

If we arrange things so that the reaction can take
place in a galvanic cell, 2 x 96,540 coulombs will pass
through the cell by the time these amounts have
reacted. These 193,080 coulombs will have given us
364,000 joules of work, and the voltage of the cell
must therefore be

364,000 volt-coulombs ^ o^ ^,
— zr:nrrz ; ; — = ^'^^ VOltS.

2 X 96,540 coulombs

This agrees closely with the measured voltage of a
cell containing this rather dilute acid as electrolyte.
While there is no doubt whatever about the cor-
rectness of this principle, there is often a great deal
of difficulty in obtaining accurate data on the heats
of reaction. In this case a number of reactions had
to be used, and the final result calculated in a round-
about way by eliminating the heats of the various

ENERGY RELATIONS 69

intermediate steps. Even in this case there is no
doubt as to the correctness of the method, but the
final result is always afflicted with a large experi-
mental error.

43. Heating and Cooling of the Cell. — The ordinary
practical storage cell contains acid of density about
1.210. It cools during discharge and heats during
charge, and can therefore not be brought under the
simple law we have just used. We can make some
qualitative statements about it, however.

Since it cools during discharge, it must take into
its system a certain amount of heat from the room
during the passage of 96,540 coulombs. At least a
part of this heat will be transformed into electrical
energy. Since we always calculate on the basis of
96,540 coulombs, the voltage of this cell must be
higher than it would be if it did not cool down while
it was working.

During charge, the cell gets hotter than the room.
A part of the energy supplied to charge it is used in
heating the surrounding objects, and it therefore
takes more energy to completely reverse the reaction
than it would if the cell did not change its tempera-
ture during charge. Since we use the same 96,540
coulombs for the reversal, the charging voltage must
be higher than it would be if the cell did not heat up.

44. The Oeneral Equation. — We can handle this
case quantitatively just as easily as the simple previ-

70 8T0BA0E BATTERIES

ous one, for we have what is called the Second Law
of Thermodynamics, which states

^^ dT

For our case

W = available electrical energy.
Q = heat of the chemical reaction.
T = the absolute temperature.

-— =s the temperature coeflBcient of available elec-
trical energy.

Since all our calculations are based on gram-equiy-
alents, 96,540 coulombs are always supposed to pass
through the cell, and the electromotive force of the
cell is therefore a measure of the available electrical
energy.

If e = the electromotive force of the cell, we can
put this formula into a form adapted specially for
the case of galvanic cells.

F being our 96,540 coulombs.

For an acid concentration corresponding to a den-
sity of 1.210 we have for Q (per gram-eqnivalent)
about 43,000 calories.

-— is positive and has a value of about 0.0003 at

20° C.

ENERGY RELATIONS 71

Numerically

e = ^^'^^^^J'^^ + [290 X 0.0008],

« = 1.86 + 0.087 = 1.95,

which is a little lower than the usual measurement
of 2.04 to 2.06 volts.

The complete derivation of the formula will be
found in the Appendix, page 255.

This is the general form of the expression for the
electromotive force of a galvanic cell in terms of the
chemical heat of reaction and the temperature coeffi-
cient of the electromotive force. It is perfectly
general and suggests many interesting things. There
are cells which warm up a good deal while they work.
These are the ones whose electromotive force de-
creases rapidly when their temperature is raised.
Others cool down, and the reverse effect is produced
on these by warming them from without. In the first
class, part of the energy of the chemical reaction is
used to heat the room. In the second class some
energy is taken from the room in the form of heat
and converted in the cell into electrical energy.
There are cells in which the heat of the chemical
reaction is zero and in which all the electrical energy
is produced at the expense of heat absorbed from
the surrounding air. These are the " concentration
cells," and they are very interesting and important

STORAGE BATTERIES

theoretically, even though none of them are used as
practical sources of current.

46. Temperature Coefficient. — The usual commercial
storage cell has a fairly large positive temperature
coefficient — about 0.0003 per Centigrade degree.
But it gains no energy from this fact because we

i-OS r

050

-IjO

_..^.^^MM .^^-^..^ ^-^^^^^^ ^iM—i^^^^ _^^.^^_^_ ^^-^.^MM. ^m^^^m^^^m ^^^m^^^

II 12

OOeiTYOf tUCTROLVTr

1.4

Fio. 22. — Change in the temperature coeflScient of the e. m. f . of a
storage cell with change in acid concentration (density).

reverse it when we charge it and lose from the
negative coeflBcient during this part of the cycle.
As far as this one factor is concerned we should
charge it as cold as possible and discharge it as hot as
possible. But as we shall see later, temperature has
much larger and more important influence on other
factors, and in comparison with them the change in

ENERGY RELATION 8 73

electromotive force with temperature is quite negli-
gible. Figure 22 shows the change in the electro-
motive force of the cell with change in acid concen-
tration, and the — — • of the formula can be taken

from this curve. At acid concentrations higher than
2 gm.-mol. per liter the curve does not fit the meas-
urements perfectly, and the values obtained by cal-
culating backward from the heats of dilution are
probably correct. The departure is not great, but
requires explanation. It may be that the more con-
centrated acid attacks and combines with the lead
sponge of the negative plate, even when no current
is passing, giving out heat, and this loss of energy
would of course mean that the electromotive force
found by measurement will be too small.

46. The Heat of Bilntion of Snlphnrio Acid. — The
determination of the heat of reaction for the mate-
rials of the storage cell was made in very dilute sul-
phuric acid. Under these conditions there would be
set free in the calorimeter, besides the heat of the
substances indicated in the equation for the cell re-
action, the heat of dilution of 2 gm.-mols. of HgSO^.
This is a considerable amount of heat, as every one
knows who has had occasion to dilute sulphuric acid
by pouring the concentrated acid into water. If we
used very dilute acid in our cells, we could also use
the heat of reaction found in the calorimeter, but

8T0BAQE BATTERIES

since we use iii practice rather concentrated acid,
we evidently cannot expect to get any more energy
than could be obtained from the heat of the cell
materialB plua the heat of dilution from pure H,SO^
to the acid concentration used in our ceil.
The curves of Figures 23 and 24 show the heat of

— ,

: "^^

1 ^

i. S

1. X

'• ^

: V

Fio. 23. — Curvo Bhowing the heat of dilution of a gram molecula of
UiSOi to various ooaoeDtrotiooB. Heat given in thousandBof calories.

dilution of sulphuric acid. Along the bottom of the
diagram of Figure 24 are given the densities of the
solutions formed, and along the top the concentra-
tion of these solutions in gram-molecules of HjSO^
per liter of solution.

The Q wliich we use in our energy formula con-
sists evidently of two parts, one being the heat of

XNSBQT RELATIONS

reaction of the materinls according to the funda-
mental cell reaction, the other the heat of dilution
to the concentration used in the cell being tested.
Since the temperature coefficient also plays a con-
siderable part in our calculations of electromotive

5 \

24. — Curve showing the he&t of dilution of HiSOi
various deoBitiea (at bottom) and to van
i.-molB. per liter (at top).

force, the easiest way of approaching the subject
seems to be to choose as our starting point an acid
concentration such that the cell has no temperature
coefficient of electromotive force. This we did by
choosing acid of density 1.044 (0,70 gm.-mol. per
liter}, and we thus made one factor constant.

76 STORAGE BATTERIES

47. Very Dilute Electrolyte. — 87,000 calories is the
total heat of reaction when acid of this density is
used in the cell, and this is already so dilute an acid
that not very much more heat could be obtained by
diluting it a great deal further. It will be seen
from the curve (Figure 24) that the difference in
the heats of dilution of 0.70 normal acid and 0.0
normal acid is small. It is only a couple of hun-
dred calories at the most. Q will therefore be about
87,200 calories for the most dilute solution in which
the cell electromotive force could be measured.

From Figure 22 we see that the temperature co-
efficient for very dilute acid is negative, and that it
is rapidly increasing in the negative direction as the
acid density approaches zero. Dolazalek has meas-
ured this coeflBcient for very dilute acid (0.0005 gm.-
mol. per liter), and he finds it about — 0.0025 volts
per Centigrade degree.

From these data we can calculate the electromotive
force of a storage cell having this very dilute acid as
electrolyte.

1.87 -0.72 = 1.15 volts,
which is close to the measured value.

ENEBQT RELATIONS

4& Conoentratad Acid. — Passing to ooucentrated
acid, the agreement between the simple theory and
the meaaurementa is not by any means so close.
This will be at once evident from an examination
of the cmres of Figures 22 and 24 in connection with

I" -y'

PERCENT OF H,BO,

the results of measurement on cells with various acid
concentration, given in the curve of Figure 25.
Measurement shows that the electromotive force of
a cell is nearly a linear function of the acid concen-
tration, only departiijg from a straight line in the
region of dilute acid, and certainly approximately
straight for all acid coucentrationB used in practice.

78 STORAGE BATTERIES

Figure 24 shows that Q decreases with increasing
acid concentration^ since the heat of dilution to be
subtracted from the constant part of Q becomes
greater and greater as the acid concentration in-
creases. On the other hand, the change in electro-
motive force with change of temperature is in the
right direction to counterbalance this only as far as
acid of density 1.15. Beyond this both the Q and

the -jj= of our energy formula are decreasing, while

the measurements show that the electromotive force
is constantly increasing.

At acid density 1.15 the formula still holds accu-
rately enough.

e =: ^y^^^.^'i^ + 290 X 0.00036,
2 X 96,540

6 = 1.85 + 0.14 = 1.99.

For the higher densities we can no longer expect
close agreement, if we take the data of our curves.
But at the usual acid density of 1.210 the agreement
is still fairly close.

e = 85,000 X 4. 18 390 x 0.00032,
2 X 96,540

6 = 1.84 + 0.093 = 1.933,

noticeably lower than the me^ured value, which is
2.06 volts.
49. This lack of agreement of course arouses sus-

ENERGY RELATIONS 79

picion of our data. The fundamental theory has
been so well and thoroughly proven in hundreds of
cases that we need hardly fear any trouble there.

While the thennochemical data for the heat of
reaction and the heat of dilution are hard to obtain
and undoubtedly fraught with considerable experi-
mental error, there is nothing in the course of the
curves expressing them to excite any suspicion of
the correctness of their general trend.

The curve connecting the temperature coefficient

of the electromotive force with the acid density

(Figure 22) is the one which seems to contain the

de
doubtful data. The droop in the value of -— = comes

^ dT

in those concentrations of acid where lead is rather
rapidly attacked and dissolved. Manufacturers have
stopped increasing the density of their electrolyte
at about 1.200, because they found local action to
be a factor just beyond that point. If there is local
action at the negative plate, and the acid is being
used up there as a result, the average density in the
cell would not be the same as that at the point of
cell activity. And since there is no current passing
when these measurements are made, diffusion alone
must replace the exhausted acid. This would cer-
tainly account for at least a part of the discrepancy,
but this still remains a point which demands further
investigation.

CHAPTER VIII

REACTIONS AT THE ELECTRODES

50. In our discussion of the action of the Daniell
cell (page 26) we decided that we could get

1.1 X 96,540 volt-coulombs

of work from the cell when 32.7 gm. of zinc went into
solution as Zn**""*" and 31.8 gm, of copper changed from
Cu"*""^ to metal. There are a great number of pos-
sible cells of the same type, for we can replace either
zinc or copper or both by any other metals immersed
in solutions of their salts, and in this way make cells
quite similar to the prototype.

51. Cells of the Daniell Type. — The following list
indicates a few of the combinations and their electro-
motive forces. These are measured with the metal
immersed in a solution which is normal with respect
to the metallic ion. The Daniell cell itself contains
65.4 gm. of Zn"''"^ per liter of solution about the anode
and 63.6 gm. of Cu++ per liter about the cathode.
Whenever we use silver as electrode, we measure it
in a silver salt solution containing 107.9 gm. of Ag"*"
per liter.

REACTIONS AT THE ELECTRODES 81

e. m. f.

Cu/Cu+VZn+VZn 1.10 Cu cathode, Zn anode

Cu/Cu+VCd+yCd 0.750 Cu cathode, Cd anode

Cu/Cu-*-+/Fe+VFe 0.986 Cu cathode, Fe anode

Cu/Cu++/Ni+VNi 0.926 Cu cathode, Ni anode

Cu/Cu+VAgVAg 0.469 Ag cathode, Cu anode

Zn/Zn++/Cd+VCd 0.360 Cd cathode, Zn anode

Zn/Zn+V*'e-*'Vi''e 0.113 Fe cathode, Zn anode

Zn/Zn+VNi+'^/Ni 0.173 Ni cathode, Zn anode

Zn/Zn+ VAgVAg 1.568 Ag cathode, Zn anode

etc.

If a very little cross-calculation is undertaken,
some interesting things will be found. We did not
need nearly all these statements to cover the facts,
for we can calculate from

Cu/Cu+VZn-*-VZn = 1.10
Cu/Cu-^-^/Cd-^yCd = 0.750
Cd/Cd+VZn++/Zn = 0.350

and others in the same way. We can also calculate
a good many combinations which we have not put
down. For example, —

Zn/Zn+VNi+VNi = 0.173

Zn/Zn-^-^/AgVAg = 1.568

Ni/Ni++/Ag+/Ag = 1.395

and in the same way for any other combination.

All these connected facts suggest a possible sim-
plification. Why not calculate the work at the two

82 STORAGE BATTERIES

electrodes separately ? For the Daniell cell : (1) the
work available when 31.8 gm, of copper changes
from ion to metal, and (2) the work available when
82.7 gm. of zinc changes from metal to ion. And
of course we would not stop here. We would go on
and determine the work available when 107.9 gm.
of silver passed a silver electrode, and so on for all
the single electrodes. Dividing the work in joules
in each case by 96,540, we would then have a series
of single electromotive forces, and from this series
we could pick out any two we wished to combine to
make a galvanic cell.

52. Standard Electrode. — Before we can begin to
make such a series we must in some way fix a value
for one single electromotive force metal/ion. There
has been a good deal of trouble in scientific circles
about this, but fortunately it does not make the least
difference for our elementary work what this stand-
ard metal/ion electrode is, or what we take for its
single electromotive force. If we should put any
one of the single metal/ion combinations equal to 1,
and then measure all the others against this, we
would arrive at exactly the same figures as those
given in our series on page 81. As a matter of fact
we have a so-called "normal electrode," and its elec-
tromotive force has been determined separately
in various ways. Measured against this single
electrode, it has been found that the electromotive

REACTIONS AT THE ELECTRODES 83

force Zn/Zn"*"** has the value 1.053 volts, the zinc

passing from metal to ion through the electrode. It

is gfiven the negative sign and is written Zn/Zn'*'"'"

= - 1.053.

Cu/Cu++ is +0.046, measured against the same

standard.

Using these values, and our series of cells of the

Daniell type, it is a very easy matter to write out a

list of the single potentials of all the metal/ion

electrodes which appear in that list.

^n?nZ -i-;''lDaniell cell 1.099
Cu/Cu++ +0.046 J

Fe/Fe++ - 0,940

Ni/Ni++ -0,880

Cd/Cd++ - 0.703

Ag/Ag+ + 0.505

and we might add from other measurements

Pb/Pb++ - 0.431
H/H+ -0.283

Hg/Hg++ - 0.467, etc.

S3i Work done at an Electrode. — So here we have
the way opened for the calculation of the work done
at each electrode. We need only to multiply the
single electromotive force by 96,540 and the result
is the number of joules furnished by that half of the
cell during the change of a gram-equivalent of the
metal to ion, or vice versa. There would not be much

84 STORAGE BATTERIES

need for any more minute theory of the process if
the single electrodes did not change their electro-
motive force considerably when the ion concentration
about them is changed. For instance, if we are
using Ag/Ag+ as one of our electrodes and silver is
going out of solution, this half of the cell furnishes
0.515 X 96,540 joules of work. But if we change
the concentration of the ion from 107.9 gm. per liter

to 10,79 gm. per liter [from iV to — j, the half cell

only furnishes 0.457 x 96,540 joules for the same

amount of silver.

At the anode a change of concentration has

the opposite efifect. Zn/Zn"*""*" iV has 1.053 volts.

N
Zn/Zn+"^— measures 1.082 volts.

Nernst has suggested a generalization which makes
the whole subject matter easy to remember and
which at the same time opens the way to many inter-
esting and important numerical relations.

54. Nemst's Theory of Solution Pressure. — Let us
think of the question in this way: Each metal has
a tendency to send ions into solution, and does it.
The ions carry with them a definite quantity of
electricity of -|- sign, for the metallic ions are all
cations. If the electric circuit is not a closed one,
this leaves the metal with — charge, and before the
concentration of ions has reached a very high value.

BE ACTION a AT THE ELECTRODES 85

a true static attraction is produced between the —
charged plate and the + charged ions in solution.
Unless this condition of things is relieved by dis-
charging the plate, the concentration of the ion in so-
lution no longer increases, and we have equilibrium.
(See Fig. 21.)

Theoretically, at least, we can reverse this process
by using a metal with a comparatively slight tend-
ency to go into solution, and placing it in a con-
centrated solution of its ion. Since a .very small
concentration of ion is necessary to balance the
solntion pressure of the metal and we have purposely
made the ionic concentration high, ion will change
to metal under these circumstances and the plate
will take on a -|- charge until static repulsion causes
equilibrium. So far this is rather hypothetical. But
measurements show that it fits the facts very closely
indeed. If a metal is going into solution as part of
a galvanic arrangement, we can better the electromo-
tive force of the cell by surrounding this anode with
an ionic concentration as small as possible. The
single electromotive force of the electrode goes up
as the solution about it is diluted. If a metal is to
go out of solution as part of a cell, we can assist it
by increasing the concentration of its ion to as high
a value as possible.

55. Electrode Equilibrinm. — A few simplifying
assumptions lead us to still more exact numerical

86 STORAGE BATTERIES

relations. Let us assume that the solution pressure
of each metal is constant and that when it dips in a
solution it is constantly held in equilibrium by a
layer of charged ions about it. Then the passage
of 96,540 coulombs through the cell results in the
change (suppose this is the anode) of a gram-equiva-
lent of metal into ions of this definite equilibrium
concentration and subsequent diffusion of these ions
from the more concentrated solution about the plate
into the njain body of the electrolyte. The whole
work of the electrode has been expended in main-
taining this ion concentration about the plate. We
can calculate the total work of the electrode as merely
the osmotic work corresponding to the change of a
gram-equivalent of the ion from its equilibrium con-
centration to the average concentration of the elec-
trolyte (see Appeudix, page 266).

56. Osmotic Work. — The osmotic work available
as the result of such a change in concentration is

i2rin§,

where O^ is the concentration in the equilibrium
layer about the electrode, C!j the concentration in the
main body of the cell, ^ is a constant for all dilute
solutions — numerically the same as the gas constant
jB, T is the absolute temperature, and In is the sign
indicating a logarithm to the natural base e.

REACTIONS AT THE ELECTRODES

Oi was the concentration which exactly balanced
the solution pressure of the metal. As far as we
are concerned we could put P, the solution pressnre
of the metal, in place of (7^, since the electrode is
in equilibrium.

Now let a gram-equivalent of the metal change to
ion and diffuse into a very large cell, in which the
ionic concentration is (7^.

The osmotic w^rk is

jRrin^,

and since a gram-equivalent has been used, 96,540
coulombs have passed through our electric circuit.
Electromotive force x 96,540 = osmotic work

The electrode electromotive force

^^ In^.

96,540 G,

If we put in the numerical values, using the gas
constant for R and changing it to joules, measuring
everything at 17° C, and changing to the ordinary
system of logarithms, we get

0.0575, P,
n being the valence of the ion.

88 STORAGE BATTERIES

This for one electrode. At the other we will have
a precisely similar set of relations except that at the
cathode the change is from ion to metal, and the
electromotive force will therefore have the opposite
sign. The electromotive force of the cell as a whole
will be the difference of the two expressions.

0.0575, P«^ 0.0575, P,
n Ca n C^

57. Effect of Concentration on Electromotive Force. —
Evidently if we want our cell to have a high electro-
motive force, we must choose

as anode, a metal with a high solution pressure ;
as cathode, a metal with a low solution pressure.
And we must also make

the ion concentration about the anode low ;
the ion concentration about the cathode high.

58. Application to Lead Accnmnlator. — In the case
of the lead accumulator we have evidently chosen
a favorable set of conditions, for it has about as high
an electromotive force as any practicable cell. It is
a matter of interest to examine this particular gal-
vanic combination from the new point of view.

No difficulty is found in applying it to the lead
plate. This is the anode during discharge, and we
can be quite sure that this electrode is reversible
with respect to the ion Pb**"*". We have insured a
low concentration of this ion in the main body of the

REACTIONS AT THE ELECTRODES 89

electrolyte, for lead sulphate is a very slightly solu-
ble substance. The only electrolyte which I can
think of that would possibly increase this single
electromotive force would be a soluble sulphide, for
lead sulphide is even less soluble than the sulphate.
For the lead plate, we have

e = 0.0288 log

59. Theory of Le Blanc. — When we examine the
peroxide plate we find it a much more difficult
matter to decide upon our active ion. Whatever it
is, it must be present in the electrolyte in exceedingly
small concentration and quite beyond the limits of
chemical analysis. Two theories have been pro-
posed, one by Le Blanc and one by Liebenow, and
while each assumes the existence and importance of
a quite different ion, the final result is much the
same in each. Le Blanc^s reasoning is in this form.
Lead peroxide has a small but perfectly definite
solubility in water, and reacts with it in the reaction

PbOa -I- 2 HjO = Pb++ -h 4 0H-,

++
forming a quadrivalent lead ion Pb"*"*", and OH" ion.

During discharge the quadrivalent lead ion changes

to ordinary lead ion Pb++, and this meets with SO^

and is precipitated as solid lead sulphate.

90 8T0BA0E BATTERIES

The entire course of discharge is therefore gfiven
by the set of equations —

PbOj -h 2 HjO = Pb*+ 4 OH-.

Pb++ + Pb^et + 2 SO4-- = 2 PbSO^,
40H- + 4H+=4H20,

and during charge these reactions are completely
reversed : —

2 PbSO^ = 2 Pb++ + 2 SO4— ,

2 Pb^+ = Pb++ + Pb„«,,

Pb++ + 4 OH- = PbOj + 2 HjO,
4 H+ + 2 SO4- = 2 HjSO^.

The total result of these reactions gives a reaction
just like our fundamental one —

Pb + PbOa + 2 HjSO^ = 2 PbSO^ + 2 HjO,

for during discharge we lose lead and lead peroxide
and gain 2 of lead sulphate and 2 of water, and dur-
ing charge the reverse change takes place. As far
as the chemical facts of the reaction are concerned,

Le Blanc's theory fits very well.

++
The quadrivalent lead ion Pb"^"*" can be shown to

exist, but we have not much data as to its concentra-
tion in the electrolyte of a lead accumulator.

60. Liebenow's Theory. — Liebenow's theory is in
several ways a more acceptable one than Le Blanc's.

BEACTIONS AT THE ELECTRODES 91

He assumes that the lead peroxide electrode is re-
versible and that the electrolyte contains PbO^ ion.
Then during discharge this ion goes into solution at
the cathode (it is a negative ion) and reacts with the
H"** ion of the acid to form Pb and water

PbOj- + 4 H+ = Pb++ + 2 HjO;

the lead ion finds SO^ ion waiting for it,

Pb++ + SO4— = PbSO^,

and precipitates as solid lead sulphate (see Figures
14 and 15).

The reaction at the anode is the same as before,
and the sum of the whole is again our fundamental
reaction.

PbO, undoubtedly does exist in perfectly meas-
urable concentration in strongly alkaline solution,
and theoretically must also be present in the acid of
the cell. In the Appendix (page 261) will be found
the complete calculation, which leads to the remark-
able result that the concentration of PbO^"" in an
ordinary cell acid is about 4 x 10"^ gm.-mols, per
liter. In the same electrolyte the concentration of
the Pb++ ion is about 2 x lO"*.

While it is true that 10"** means only a few mole-
cules in a volume equal to the oceans of the world,
this is the number we need to express the concentra-
tion ratio in our cell. It must be remembered that

92 STORAGE BATTERIES

these ions only have to pass over molecular distances
and that the reservoir of sulphate from which they
are drawn can supply them as fast as they are needed.
In such statistical matters as this the unit may make
a great difference. There is nothing surprising
about the statement that ten children are born per
year in a certain village. The same fact is repre-
sented by the statement that 0.00000031 children are
born there per second.

In terms of Nernst's theory and Liebenow's
hypothesis, we have for the lead peroxide electrode

^Pbo.= -0.0288 log/

pi>o.

and for the entire cell

e = 0.0288 log /n>^pbo, .

6L Clonclusions to be Drawn. — This equation gives
interesting qualitative relations. Evidently we can
hardly do better than to retain sulphuric acid as our
electrolyte. We are also to use it as strong as the
life of the plates will permit ; for while lead sulphate
is more soluble in concentrated acid than in dilute,
and we will therefore lose a little at the lead elec-
trode, the PbOj concentration decreases as the
fourth power of the hydrogen ion concentration, and
we should much more than make up for the loss.
As a matter of fact, manufacturers have gradually

BEACTI0N8 AT THE SLECTB0DE8

increased the commercial concentration of their elec-
trolyte, with a corresponding increase in the electro-
motive force of their cells. Ten years ago electrolyte
of density 1.15 was the rule. Now nearly every one
uses a density of 1.210, and for special work as high
as 1.225. In portable cells where the limit of weight
is fixed and a small total mass of electrolyte must be
carried, the density is permitted to go as high as 1.27.
We can also see from this formula that an alkaline
electrolyte, with its high concentration of PbO^ — ,
would greatly decrease the electromotive force of
the cell. In caustic soda solution it does in fact go
as low as 0,75 volt. An electrolyte containing a
large concentration of Pb**"*" will also lower the elec-
tromotive force, and if we could manage an electro-
lyte which was both strongly alkaline and high in
Pb"*"*", we could reach a very low value indeed.

CHAPTER IX

CHARGE AND DISCHARGE

62. Up to now we have been considering the cell
as independent of the current flowing through it.
This point of view is necessary for a theoretical dis-
cussion, because the whole cell is changed as soon as
current passes. From a rather simple system, quite
open to formal investigation as long as it stands on
open circuit, the cell changes to a very complex
system as soon as it begins to work. The only way
to study this complicated thing is to keep all the
factors but one as constant as possible, and follow the
change in that one. Each factor in turn can some-
times be taken up in this way and the whole problem
cleared up. But in the case of our cell we shall find
that this general method of solving scientific puzzles
is hard to apply. So many of the factors which are
active in a storage cell are not within our direct con-
trol. For these reasons it is easiest to follow 4;he
changes in an accumulator by study of onrves and
families of curves. A single such curve shows the
mutual effect of two things. A family of curves
shows a great deal about three factors and their re-

CHARGE AND DISCHARGE 95

lations. Let us take first of all the curves which
show how the voltage of an accumulator changes
with time, while it is being charged and discharged
at a constant rate.

In all that follows, the general theory of Chap-
ter VIII should be kept clearly in mind. Large
changes in voltage appear during complete charge
and discharge, but every change can be explained
satisfactorily and completely by reference to changes
in the eonoentration of the active ions.

The electromotive force of the Pb/Pb++ electrode
is gfiven by the formula —

€p5 = 0.0288 log

-* Pb

Cpb+ +

and that of the PbOj/PbOj — electrode by —

«Pbo. = 0.0288 log -^^^^

at every point of a charge, discharge, or recovery
curve.

The only variables are the concentrations of Pb"*"*"
and PbOa~.

It should also be kept clearly in mind that the
Pb*"*" ion concentration varies inversely as the acid
concentration at the point of activity, and inversely
as the square of the H^ ion concentration, while the
PbOj ion concentration varies inversely as the

96 8T0BA0E BATTERIES

square of the acid concentration and therefore in-
versely as the fourth power of the H* concentration
(see Appendix, page 260, for the complete state-
ment of the theory).

63. Charge Carve. — Our cell has been fully dis-
charged at a rather low rate. Lead sulphate has
been formed through each, plate wherever sulphuric
acid of sufficient concentration was available for re-
action. Lead peroxide and lead sponge have been
more or less completely exhausted and partially
covered with a layer of sulphate. Sulphuric acid
has been taken from the electrolyte, which has a
lower acid concentration than before the discharge.

We connect the terminals of the cell with a source
of current, and proceed to charge it.

The reaction is

2 PbS04 + 2 HjO = PbOj -h Pb + 2 HjSO^.

The reservoir of lead sulphate supplies material,
and water is taken from the electrolyte as well.
The reactions described on page 55 begin, and sul-
phuric acid is set free in the two plates.

If the cell has been recently discharged, this reaction
begins immediately, and the voltage rises slowly
until diffusion balances the concentration of the acid
at the point where the reaction is taking place. But
if the cell has been rather completely discharged,
and has been standing for some time, the layer of

CHARGE AND DISCBARGE

sulphate, which has had time to change into the
firmer and more stable modifications, must first be
broken through. In this case the charging voltage
overshoots a little just at first (Figure 26). It rises
rapidly for a short time, and then drops again slowly
to the value corresponding to the concentration of

111!!

the acid at the active point in the plate (see A,
Figure 27). There is no positive evidence that this
kind of lead euphate is an insulator or even a very
poor conductor. Measurements of the internal re-
sistance of a discharged cell show that there is no
increase at this point sufficient to account for this
little rise in voltage. It seems much more probable

STORAGE BATTERIES

that the acid concentration is, as usual, responsible,
and that the layer of sulphate merely prevents easy
diffusion until it has been broken through. It may
act for the moment as a semi- or nearly impermeable
membrane, retaining the concentrated acid, and so
causing the rise in electromotive force.

F .

A B

,_-

^--

\ -^

HOURS

Fxo. 27. — Changes in cell e. m. f. during charge and discharge at the

5-hour rate.

In any case the electromotive force of our cell
very soon reaches a definite value, characterized by

the factors : —

(a) Acid density.

(J) Temperature.

(d) Type of plate.

(e) Previous history.

CHARGE AND DISCHARGE 99

64. Peonliaritiet of the Charge Curve. — At the point
marked B on the charge curve (Figure 27) this
definite condition has been reached. The condition
is only momentary, and, as charge proceeds at con-
stant rate, the electromotive force increases slowly
throughout the part of the curve marked 0. Sulphate
is being transformed into lead and peroxide, and acid is
being produced throughout the plates. Diffusion is
becoming more and more difficult, for it must take
place through ever-increasing distances, and along tor-
tuous and minute passages. The slope at any point in
this part of the curve is also a function of the five fac-
tors, and the condition of the cell as to charge can
always be seen by one acquainted with the type of
plate, by merely reading the voltmeter, and taking
into account the time the cell has been on charge.

At D there comes an evident change. The curve
begins to rise much more rapidly, and gas is evolved
more freely. The curve rises through jF, then drops
slightly at F^ and runs along parallel to the time
axis. From this time on the cell is merely a machine
for the electrolytic manufacture of hydrogen and
oxygen.

The rapid change of curvature at D is significant.
It cannot be due to any further increase in the acid
concentration inside the plates, for they are nearly
completely changed into lead and peroxide by now,
and very little acid is being formed. What little is

100 STORAGE BATTERIES

formed is greatly assisted in circulation and dilution
by the gas bubbles now rising from the plates. This
acts as a vigorous stirrer and equalizes the acid con-
centration through the whole cell. The rapid rise at
D must have another cause. Refer to the equation
on page 89.

Up to the point D we had plenty of lead sulphate
to work on, and the solution has always been
thoroughly saturated with PbS04, except perhaps
immediately about the grains on which Pb and PbOj
are depositing. But at D we begin to clear out the
last of the solid sulphate and from that point on the
solution becomes less and less concentrated in Pb'**"^.
Part way up the curve at JE there is so little Pb+"*" pres-
ent that it is just as easy to cause hydrogen gas to
leave the solution as it is to force out solid lead.
This means a high electromotive force (page 92) . At
JE the last of the more concentrated acid and of lead
ion as well hold up the electromotive force for an in-
stant by their presence inside the plates ; they are
then cleared away by streams of gas bubbles, and the
charge is complete.

65. Now for the factors a, i, c^ d, and e, and their
effect on the charge curve.

(a) Acid density. The effect of various concentra-
tions of acid on the open circuit electromotive force
of the cell is shown in Figure 25. The effect at any
point in the charge curve might also be found, but

CHARGE AND DISCHARGE 101

it would be so very lively and changeable a factor
as not to be very valuable as a criterion. From
what we have already learned of the effect of acid
concentration on electromotive force (page 92) we
can be sure that something like the following picture
expresses the factor in question. Diffusion is a func-
tion of gradient. Acid will diffuse out of the plate
into the ambient electrolyte at a rate proportional to
the difference of concentration at these two places.
But acid is produced in the interior of the plate in
direct proportion to the current which is passing, and
regardless of acid density In the electrolyte. The
same current will therefore give a greater gradient
with a weaker acid in the cell than with a strong one,
and the effect of the average acid on the electromotive
force will be less for high than for low concentrations.
(6) Temperature. , This has an important effect
on diffusion. At the higher temperature diffusion
is rapid, and the concentrated acid formed in the
plate is rapidly removed. The voltage required to
charge our cell will be lower and the whole charge
curve will be changed in position and shape. This
effect is, of course, quite aside from any effect of
temperature on the electromotive force of the cell (see
page 72), and the latter factor is for any practical cell
so small as to be almost negligible, while the former
factor is by no means a small one. The temperature
coeflScient of diffusion is about 2 % per Centigrade de-

102

STORAGE BATTERIES

gree and is for certain types of cell of great importance.
In electric vehicle work, for instance, winter tempera-
tures are most trying, and the effect is to reduce the
apparent capacity of the battery by a considerable
fraction. This almost wholly because of voltage
limits imposed by the slowness of diffusion at the

tJO

1 2 i 4 i e 7 a

H0UR9

Fia. 28. — Charge curves on the sam6 plate at various rates.

low temperature. (See page 253 for data on practical
cells.)

(c) Rate of charge. This determines the rate at
which acid is formed at the place where the action is
going on. Diffusion determines how fast this acid
shall be removed. At higli rates the whole charge
curve is steeper. (See Figure 28.)

(d) Type of plate. The position and slope of the
charge curve vary with the plate tested. Surface,
thickness of active material, hardness, are all factors.

CHAROB AND DIBCHARQE

103

A large-surface Plante plate, with a comparatively
small couteDt of active material, shows a curve like
A in Figure 29. An intermediate type has the
characteristics shown by B, in the same figure. The
extreme of high capacity, a light grid with a large

^-^^^

(tf — ' —

rwns

Fia. 20. — ChitrKe curves for plat«B of various types.
A. Flouts plat«B. B. Mixed type. C. Paste plates.

percentage of active material, gives curve 0; all other
factors of course being constant for the three cases.
Here, as in every other case, the concentration of
acid at the point of action is the deciding factor.
The large surface plate is pretty freely open to the
acid. Diffusion is easy, since it takes place lai^ely
through the main body of the electrolyte and not
through the pores of a packed masa of active material.
In the masa plate we have the other extreme.

104

8T0BA0S BATTBBIB8

Diffusion, except at the v.ery outside surfaces, must
proceed through long capillaries in a comparatively-
thick mass of active material and is correspondingly
slow and inefficient.

66. Recovery after Charge. — pur cell is fully
charged. The last remnants of available lead sul-

c«a

TOf

JCl

""■

„

— CWVB bI

phate have been attacked and removed and the plate
is nearly pure lead or lead peroxide. Whatever
sulphate is left in the plate lies too deep to be easily
reached or is incapsulated with active material.
When the charge circuit is broken the electromotive
force drops along a reoovery ourre. Lead sulphate
will now go into solution until saturation is reached,
and the process of solution of the sulphate in the
quiet electrolyte is largely one of diffusion. The

CEABOE AND DiaCBABOB

105

carve 18 very much like a diffusion curve, dropping
rapidly at first and then raore and more slowly
toward a limit. (See Figure 30.)

67. Siwharge. — If curreut be now drawn from the
cell by closing the circuit through an external resist-

l„"h

« t^-^"

"Jv^

Figure 27.

snce, the electromotive force passes through the
stages shown in the curve of Figure 27. The little
hump in the curve at (? (see Fig. 31) appears only
under certain conditions, and it may be due to the
formation of a supersaturated Pb'^'^ solution and a cor-
respondingly low electromotive force. This could

106 STORAGE BATTERIES

occur in very fully charged plates where there is not
enough lead sulphate near the surface to release such
a supersaturation. And, as a matter of fact, it only
does appear in fresh and active plates which have
been very fully charged immediately previous to tak-
ing the discharge curve. This peculiar twist can last
but an instant, for then the limit of supersaturation
is passed and PbSO^ begins to deposit everywhere.
The electromotive force then rises to its proper value,
corresponding to the concentration of the acid (now
being depleted) at the point of activity, and the curve
proceeds smoothly. As discharge goes on along the
curve at 5", diffusion (now of acid into the plate) be-
comes more and more diflScult. The active concen-
tration of acid droops, and at the point I the cell is
for practical purposes discharged. Its electromotive
force is still 1.7 volts, and it could be run for some
time longer at low rates before dropping to zero. As
storage batteries are used in practice, 1.7 may be
taken as the limit of useful discharge at a low rate.
(See page 118.)

The five factors of page 27 are just as important
during discharge as during charge and for the reasons
given at that place. Acid density determines starting
point and position of the curve, and simultaneous ex-
amination of discharge voltage and density, as given
in the curves of Figure 32, enables one to decide upon
the condition of the cell as to charge or discharge

CBABOB AND DIBCSARQE

'ik^

>««

■v

^
\

n acid density and in
voltagD.

from acitl density as well as from voltage. Temper-
ature affects diffusion and therefore acid concentra-
tion at point of action and electromotive force. It

—

ITOPI

Ro. 33. — Eiul of diocharge and reooTeiy.

108

STORAGE BATTEBIES

also afFectfi the electromotive force directly. Rate of
discharge determines acid concentration and there-
fore the concentration of the active ions. Type of

IOC

lis

IN 5

MRS

T II-

1 ■

I.+

(TO

Fra. :

— Reoovety after vety 'ous and complete diiebarcg.

(See

plate enters and previous history of the cell,
page 113.)

68. EeooTery after Sucharge. — The curve along
which recovery takes place after discharge is shown
in Figures 33 and 34. It is very much like a diffu-
sion curve, and represents the rate of return to the

CHARGE AND DISCHABQE

109

normal concentrat^ion of acid in the cell on the part of
the acid in the deep interstices of the plates. It is
not quite the right shape for a pure diffusion curve,
and the equalization of concentrations throughout
the cell is undoubtedly assisted by local action.

2.4

Ij 2i)
S

—

2 3

HOURS

Fig. 35. — Charge and discharge curves of \A\ Plants and \B\ mass

plates.

G9. Spedal Pecnliaritiefl of Charge and Disoharge
Carves. — The two extreme types of plate — large sur-
face Plants on the one hand, and thick mass plates on
the other — show evident differences in their curves
of operation. Figure 35 indicates the general char-
acter of these differences, and a resume of the theory
of the inflections of these curves will be found to

110

BTORAOE BATTSmSa

agree with the physical characteristics of the plates.
It is quite possible to get composite curves from
composite plates. An interesting example is the
type of ribbed Plante plate now very common all
over the world and used for tlie hardest kind of

■^

i 3

i 6

S 9

Fio. 36. — Full dJBcharge curve of ribbed PlaDti plate.

work. Figure 36 shows tlie full discharge curve of
a Gould plate. For the greater part of its discharge
it behitves like a large surface plate, which it is.
Then the action reaches that part of the plate where
there is a considerable mass of active material, much
of it at about the same distance from the main bulk of
acid in the cells. Hero the droop is stopped for a
short time, and only when the action has penetrated

CHARGE AND DISCBAROB

111

far into this last reservoir of material does the final
drop begin. And the final drop, instead of being
like that of a large surface plate, is much more like
a mass plate. The only reason wliy these peculiari-
ties are not noticed every day is because they lie at

1 4

1. ^

K \

^"^=^

voltages lower than those of practical service condi-
tions. (See also Fig. 37.)

70. Cliarge and Discharge at VarioQ* £at«s. — Figures
38 and 39 show si^rius of curves of charge and dis-
charge for two types of plates at various rates. They
hardly require detailed discussion, for tliey fit very
closely the general {>rinciples so often invoked in

112

STORAGE BATTERIES

explanation of changes in cell electromotive force.
The charge curves have much the same general char-

nouns

Fig. 38. '— Curves of operation of Plants plates at various rates.

The rates for the curves of Figure 38 are

For 8-hours of charge or discharge 1 ampere
6 „ „ 1.4

3 ,, „ 2.0

1 „ „ 4.0

21) minutes ,, 8.0

5 minutes ., 16.0

II
II
II

These are the rates usually specified in practice.
The capacities corresponding to these rates are

For 8-hour charge or discharge 8 ampere-hours

»5 II »i 7

3 ,, „ 6

1 ,1 .1 4

20 minutes ,y 2.67

5 minutes ,, 1.33

11
II
II

acteristics at different rates, but show more rapid
changes as the rates are raised. The most interest-

CBABOB AND DISCHABOB

118

ing thing about tlie set of curves is the information
it gives about the last factor in our list — the " pre-
vious history " of the cell. It makes a great differ-
enoe in the discharge curve of a cell whether the cell
has been charged at a high or a low rate, and just as
great a difference in the charging curve, whether the

—

—,

Fio. 39. — Curve* of operation of maaa platea at variotu rates,
previous dischatge has been fast or slow. Take a
single case. Suppose a fully charged cell has been
discharged at the 5-minute rate. It is evident from
the figure that only 1.3 ampere-hours have been drawn
from it. We ouly need to return a Uttle more than
this to the cell to charge it completely. In the same
way, if our cell has been completely discharged at a
low rate, and then charged at the 5-minute rate, we
can only get about 1.3 ampere-hours into it. It may
be fully charged for a 5-minute discharge, but it is

114

STORAGE BATTERIES

by no means fully charged for a 3-hour discharge.
When we come to the chapter on operation we shall
have another side of this same problem to look at —
the one which deals with the effect of charge and dis-
charge rates on the life of the cell.

*.4
10

•

♦

CHARGE
QHAR6E

-.Bfcni

isr —

-^A

,^^~~

♦

OISCHA

, ^

•*

1 f

\ I

( <

k 1

f t

1 •

HOURS

Fig. 40. — Charge and discharge curves. Peroxide and lead plates
measured against an auxiliary electrode Gead plate).

71. ITse of Auxiliary Electrode. — It is very fre-
quently desirable to segregate the two plates in a
cell, so that the course of charge and discharge may
be followed for each separately. Several forms of
auxiliary electrode have been suggested, and the one
in most common use is metallic cadmium. A stick
of this metal is used as one electrode, and the electro-

CHAROE AND DI8CHAR0E

115

motive force Cd/dilute 0(1+"*' against one of the plates
is measured.

It is evident that this is not the most stable of
electrodes, for its readings are dependent on the
amount of current flowing through the cadmium cir-
cuit and also on temperature and other factors. It
answers very well for most practical purposes, howr
ever, and some of the curves for single plate poten-
tials which are given in this book were made with
its aid.

Another way of following the single electromotive
forces at the two plates is to use an idle lead or per-
oxide plate as a third electrode, measuring each of
the working plates against it. Figure 40 gives
charge and discharge curves for working positive
and negative plates, measured against an idle lead
plate.

CHAPTER X

CAPACITY

In our observations on the curves of charge and
discharge we found that at least five factors were
active in fixing the shape and position of these
curves. These same factors, together with the limit
of voltage set by practical experience, determine the
capacity of a storage cell in the sense in which this
term is usually applied.

The lower limit of voltage — the point to which
the cell is discharged in actual service — is not by
any means invariable. At low rates, as in telephone
and train lighting service, it is about 1.8 volts. In
regulating power plant loads, and in much of the
other regular work which a battery does, it is about
1.7. At very high rates, as when an emergency
battery is called upon to take the entire load of
a large station, it may be carried as low as 1
volt. Just for the present we will assume 1.7 volts
as the limit below which we cannot usefully discharge
our cell, and we will base its capacity on this point.

72. Faraday's Law and Capacity. — Of course ca-
pacity, in the basic sense of the word, is given by

116

CAPACITY 117

Faraday's law, and can be calculated directly from
the equation

Pb + PbOj + 2 HjSO^ = 2 PbSO^ + 2 HjO.

207 gm. of lead sponge 1

239 gm. of lead peroxide > give 2 x 96,540 coulombs,

196 gm. of sulphuric acid J

and if we keep the current small enough, it might

be possible to get this theoretical current yield at

2 volts.

Since one ampere-hour is 3600 coulombs, we will
need for one ampere-hour, 3.86 gm. lead, 4.45 gm.
lead peroxide, and 3.6 gm. HjSO^, and these are the
amounts of active materials which are really used
up in any storage cell during the passage of current
to the amount of one ampere-hour. In actual prac-
tice the voltage of the cell would have fallen to zero
long before all the material in the plates and the
electrolyte had been acted upon, and in any actual
cell there is always a very large excess of all three
of the constituents, even at the time when the cell
is "discharged." Besides, there must always be
supports for the. active lead and lead peroxide, and
these supports must in practice have strength and
weight enough to enable them to withstand many
complete cycles of charge and discharge. As we
shall see later, there are useful types of cells in
which the materials which really enter into reaction

118

STORAGE BATTERIES

only make up 10 or 15 % of the total weight of the
plates, and only 6 or 7 % of the total weight of the
installation.

73. End Voltage determines Capacity. — There is no
doubt whatever about our oft-repeated fundamental
principle that it is the acid concentration within the

g 18

Ift

^ -

—

■

E ^

)

I i

1 1

► '

S 1

r t

i 9

OISCHARGC TIME-(HOURS)

Fio. 41. — Discharge curves at various rates.

pores of the plates, at the point where the action is
taking place, which determines the voltage of the
cell. At a high rate of discharge, the acid density
at the active point in the plate is low, and the vol-
tage curve drops after a comparatively short time.
It becomes too hard for the electrolyte to get to any
more active material, even though tliere is plenty
in the plates, and useful discharge must be stopped.
Figure 41 gives a set of discharge curves made

CAPACITY

119

in actual test on a large cell. This cell was charged
each time at a constant and low rate, in order that
the chai^ng part of the cycle might not be a vari-
able factor. It was then discharged at constant
temperature at the rates given. If we take as the

<•-

„

voltage for stopping discharge 1.70 for most of the
curves, and 1.65 for the 1 hr., and 1.6 for the 20 min.
discharges, we get the following table : —

120

STOnAGS BATTERIBS

These values can be equally well expressed by means
of a single curve, for there are really only two things
to be related, — current and time. The expression of
the capacity in a separate column is merely for the
sake of having a direct statement of capacity.
Figure 42 contains this curve. It is the one which
is drawn as a full line.

^^^^

AMPERE-HOURS DISCHARGED
Fro. 43. — EKscliarge curves of Plantfi platee at the 1, 3, snd S-hour

Figure 43 gives discharge curves for Plants plates
at various rates, Figure 44 similar curves for semi-
Plant4 plates, and Figure 45 curves for thick mass
plates. In the three cases plates were chosen with
the same capacity at a medium rate of discharge (3
hours). It is evident that the large surface Plants
plates are best at the high (1-hour) rate, and that
they are by no means up to either of the other types

—

•--,

--~.

AMPERE-HOURS DISCHARGED
Fio. M. — Diochargo cuivea of semi-Plant^ plates at variouE ratea.

at the low (8-hour) rate. At the 15-hour rate the
carve for this particular plate is not shown in the

AMPERE-HOURS DISCHARGED
Fra. 46. — DiBcharge curves of thick maga plates at various

figure. It would reach 1.8 volts at about I
the horizontal axis.

—

—.

Il^ll;

■^

•^

~-v

122

BTORAQB BATTERIES

The masB plates of Figure 45 are very short of
capacity at the 1-hour rate, but they are far better
than the Plante type at the low (15-hour) discharge.

The semi-Plant^ plate lies between the other two.

■>

--r-

■

-K

— -

—

THCKNCSS M MILUUETCRG

Fta. 46. — Capacity aa a function of the thickncas of a paste plato,

at various rates. Peroxide plates asainst auxiliscy electrode.

The useful end voltage has been placed at 1.8 volts
in this case.

It is evident from these curves that the thickness
(and structure generally) of a plate is a factor of im-
portance in its working capacity. Experiments with
paste plates of the same surface and varying thick-
ness give the results shown in Figures 46 and 47, the
former for positive plates and the latter for negative.

The five currea in each figure ere for different
rates, from 1 to 16 amperes.

- 27^

^/^^

- JaV

- %V'

-/a/ ^

iV ^^^

It^

^, — iT

THICKNESS W MILUMETERS

The dottedline in Figure 46 is for an infinitely slow
rate — capacity directly proportional to thickness.

124 STORAGE BATTERIES

74. Formula for calculating Capacity at Various Bates.

— It is usually possible to find a not very compli-
cated mathematical formula to fit a curve which
looks like Figure 42 and the dotted line in this figure
is plotted as an expression of the formula

rt= constant.

n for this particular type of plate is 1.45, and the
constant is determined by putting in the actual
values for our plate at one rate and solving the
equation. See 75, below.

This exponent n is rather a good measure of the
physical qualities of a plate. It is large for thick,
dense, massive ones and becomes smaller and smaller
as the plate is given a larger surface in proportion
to its content of active material. It goes as high
as 2.0 for some plates of the most thick and tender
kind, and as low as 1.20 for the most active types of
large surface plates. See also Figure 48. A little
calculation will show what kind of a family of dis-
charge curves at different rates will be characteristic
of each of these extremes. The one with exponent
2.0 is the easiest to calculate.

75. Let us go through the course of the calculation
of such a curve for the simple case where n = 2.0.
Assuming that the cell gives 10 amperes for 8 hr.

iH = constant
102 X 8 = constant

CAPACFFT

1
f

1
/

■^i

liJ

...

— ■

—

fMjO

'f/^

/
r

' 1

1
I

/
/

2 4 6 8 10 l£ 14 16 le £0

HOURS FOR COMPITTE DISCHARGE.
Fra. 48.

126

STORAGE BATTERIES

es3

< = 1

and from this, when,

current is = 10,
current is= 16.3,
current is = 28.2,
current is = 49,
current is = 98,

iH, = 800
{2x3 = 800

ta = 267
^ = 800
ia = 2400
»a=9600

f = 16.3

i=28.2
t = 49

t=:98

capacity is 80.
capacity is 49.
capacity is 28.2.
capacity is 16.3.
capacity is 8.2.

If capacity is plotted vertically in place of current^
the family of curves for various exponents becomes
still more expressive. Figure 48 gives the calculated
curves for values of n from 1.10 to 2.0.

It is also possible to derive a curve like the one in
Figure 42 with the aid of the theory of diffusion, but
the assumptions necessary are far-reaching, and the
final formula is in fact only an empirical one like our
own. Diffusion has the chief role to play, however,
here as at every other point in the theory of the lead
(and any other) accumulator.

76. Liebenow's Diffusion Experiment. — Liebenow,
one of the most brilliant of the students of the lead
cell, made an interesting experiment on the effect of
merely allowing acid to flow through a plate which
was discharging. His arrangement is shown in

CAPACITY

127

Figure 49. A uegative plate was used in his test, and
it was found that without flow it gave 14.4 ampere-
hours. With flow it gave 41.6 ampere-hours. Such
experiments have frequently been performed of late,
and it is a most interest-
ing thing to see a plate
which haa been ex-
hausted without flow, BO
that its voltage is zero,
pick up and come to life
again as soon as acid be-
gins to flow through it.
Its voltage rises to
nearly 1.7, and it is ca-
pable of doing a great
deal more work.

The object of the flow
through the plate is to
keep the acid concentra-
tion np daring diMharge
and down during charge
at the place in the plate
where the reaction is actually taking place. Practi-
cal applications are numerous. Large surface plates
are necessary where charge and discharge rates are
high. They contain much less total active material
than paste plates of the same weight, but the material
in them is in a thin layer, and diffusion is easy to all

FiQ. 49. — Liebcnow'B eiimrimcnt
to show the effect of forcing elco-
trolyte tbraUBb the plate during
operation.

128 STORAGE BATTERIES

parts of it. Then, too, thin paste plates give a far
larger capacity per weight than thick ones operating
on the same rates and to the same end voltages.
Aids to diffusion are perhaps the most important
improvements which can be made in storage battery
work with the exception of the all-important one of
a reasonably long life under hard service conditions.

The positive plate needs help more than the nega-
tive, for besides using up or producing sulphurio
acid, water appears or disappears at that point.
It will be seen that it needs help 1.6 times as
badly as the negative. In spite of this need it is
harder to send it the necessary relief; for while
negative plates can be made both tough and porous,
the positive active material, lead peroxide, persists
in being merely a dense but rather loosely inter-
locked mass of fine grains. Some rather rough
measurements on the rate at which acid diffuses into
positive and negative paste plates are given in Figure
50. These are resting plates,, however, and do not
take into account the greater need for acid of the
peroxide plate during action.

Lead grows on the negative plate as real trees and
sponges, and this can often be clearly seen in vener-
able negatives on which the lead has been deposited
and redissolved thousands of times. The positives in
the same cells look lean, for they have lost much of
their original material, and if they are healthy, and

CAPACITY 129

of the kind that havB proven themselves capable of
hard work, they have manufactured more active
material to take the place of that lost. It is easy to
apply Liebenow's principle to the negative plate. It

Fio. 60. — Diflu^OD into restias positive and negative platca.

is much harder to persuade acid to flow through one
of lead peroxide.

77. Diffudon. — To digress for a moment to the
general subject of diffusion. A substance in solu-
tion can move about from point to point in either
of two ways — by convection or by diffusion. The
difference in velocity with which a given amount
of a substance can be transported from one place

130 STORAGE BATTERIES

to another by the two methods is enormous. Sup-
pose a tall cylinder with a couple of inches of a
strong solution of a colored salt (copper nitrate, for
example) in the bottom, and with pure water filling
the rest of the cylinder. By convection we could
mix the whole to a homogeneous average solution
in ten seconds, by violent stirring or shaking. By
diffusion alone the same degree of mixing would
take months.

The process of convection could be delayed in the
cylinder by filling it with glass or cotton wool. In
this case the transfer of material from the concen-
trated solution out through the dilute one has to
take place through spaces in the inert substances.
It is much as though the cylinder were a mile long
instead of a foot. Diffusion will also be delayed
by the inert filling, but in much less degree. The
difference becomes still more evident if we fill the
cylinder, not with pure water solutions, but with
solutions which set to a jelly, such as gelatine or
agar — a concentrated gel below; a pure water gel
above. Now convection is entirely stopped and
diffusion has all the work of transportation to do.
The process becomes a very tedious one indeed.

78. Diffusion and Convection in the Cell. — In the
storage battery the real transport of all material is
a matter of diffusion. Solid material is there in
plenty, but the acid of the electrolyte is just as

CAPACITY 131

necessary for the reaction as the solids, and it has
to come to the solid by diffusion through the fine
pores of the active material. At certain portions
of the cell cycle convection comes along to help,
especially when gas is being evolved in the plates.
The gas bubbles stir everything up and assist greatly
in bringing materials to the point where they are
needed. The difference in density between the con-
centrated acid formed during charge and the aver-
age acid of the cell also gives rise to convection
currents, which can be clearly seen by looking across
the face of a plate toward a bright source of light..
If the cell is charging, a thin stream of denser elec-
trolyte can be seen running down the face of the plate
and curling up on the bottom of the cell. The more
dilute acid can also be seen rising up along the face
of the plate during discharge.

79. Becovery Carves and Diffusion Corves. — The
curves in Figures 30, 33, and 34 are very nearly like
diffusion curves. When the circuit is closed for dis-
charge, material is rapidly exhausted near the solid
particles which are active. The concentration gradi-
ent becomes steep and acid begins to diffuse toward
that point. Lead sulphate is formed in the solution
and presently a state of very dynamic equilibrium is
reached. Acid is being transported by diffusion just
fast enough to supply the demand at the point of
reaction ; and lead sulphate is being removed by pre-

132 STORAGE BATTERIES

cipitation as fast as it is formed. The curves re-
ferred to are, of course, voltage curves, but the
relations of page 92 show clearly that the curves
can equally well express the average concentration
of reacting materials at the point of action. The
recovery curve of page 133 is of the same nature. At
the lower part, at the beginning of the recovery curve
in Figure 33, we have the final condition described
above. Materials are being supplied at a rate just
able to maintain the concentration at a rather low
and constantly decreasing value. When the circuit
is opened, consumption of material ceases. But the
concentration at the point where the reaction was
going on was different from that outside in the body
of the cell. Diffusion, therefore, continues and the
concentration differences become smaller until diffu-
sion becomes indefinitely slow.

Theoretically these curves take an infinite time to
become perfectly flat, but practically they approach
very near to a final value within a few minutes. One
exception to this last statement will occur to every
one who watches storage cells closely. A very fully
charged cell, which has been gasing freely, takes a
long time to return to its open circuit electromotive
force (see Fig. 51). This cannot be due to any high
concentration of acid in the pores of the plates, for
practically all the materials have long since been dis-
posed of and only an infinitesimal amount of acid is

CAPACITT 133

being produced. There is another reason for this
alow approach to the normal open-circuit voltage.
At the end of full charge, practically all the dissolved
sulphate has been driven out of solution. Opening
the circuit at the end of such a charge permits lead

5",-

FlO. 51. — Recovery curve after complete charge.

sulphate to form. Local action takes place at the
places where support and active material are in con-
tact. So lead sulphate is soon present inside the
plate. But before it reaches its normal maximum
concentration at all points in the plate it has to
saturate the entire electrolyte. The drop in voltage
is therefore not so rapid as it would be if only acid
diffusion were to be considered. Besides the diffu-
sion of an already dissolved substance, we have to
wait in tbia case for its formation.

184

STORAGE BATTERIES

80. The Effect of Temperatiire on Capacity. — Since
capacity is determined by a fixed voltage limit as
well as by other factors, we must expect to fiad that
the effect of temperature will be a considerable one.
Figure 52 gives a set of discharge curves at the same
rate but at the different temperatures indicated on

=:=

—

■^

■--,

■>^

{

Fia. 52. — Discharge c<

a rate but at T

the curves. This was taken with constant charge
conditions. The cell was in every case charged at
25° C. Its temperature was then changed by heat-
ing or cooling tlie thermostat in which it was kept,
and after remaining constant for five or six hours,
charging at a low rate all the time, the discharge wa^
taken. The rate was such as should give complete

CAPACITT 136

discharge in one hour under normal conditions of
service, and the 25° curve shows this. The voltage
dropped to 1.7 in just about one hour. At 48° the
dame cell ran for an hour and three quarters; at 8°
for half an hour. A difference of over 100 % for
quite possible limits of temperature, and of over
300 % within temperatures not really dangerous to
the life of these cells I

This is a very high temperature coefl&cient, to be
sure, but it is hardly possible to make a cell which
has not a coefficient of at least one per cent per
degree in the ordinary working range of tempera-
tures.

Everything combines to make the storage cell work
better and more efficiently at the higher temperature.
For the usual acid concentration the temperature co-
efficient of electromotive force is. positive, and has a
value not far from 0.0003 volt per Centigrade degree.
This, of course, has nothing to do with the ampere-
hour capacity of the cell, except to raise the voltage
a little, and thus lengthen the time of discharge a
little. Examination of the discharge curves at
various temperatures will show how very little this
affects the total number of ampere-hours which can
be taken from the cell. A difference of 30° C. means
0.0003 X 30, or a rise of only 0.009 volt in the
fundamental cell electromotive force due to the
higher temperature, and this is not even measurable

136 STORAGE BATTERIES

on a curve which is drooping as rapidly as the low-
temperature curves of Figure 52.

81. Reaction Velocity. — But the other two factors

are highly important. One of these is the diffusion,

■

which we have discussed at length. The other is not
less important, probably, though it is much more
difficult to isolate and examine. This is the increased
reaction velocity. Whatever the reactions which are
basic for the action of the cell, we have found very
good evidence that the transport through the elec-
trodes is cared for by ions which are present in very
small concentration.

The velocity with which these ions are formed from
the solid material of the plates, in reaction with the
electrolyte, is a determining factor of importance.
As a matter of fact the temperature effect on the cell
is too great to be ascribed to diffusion alone. And
while in most cases reactions between ions take
place so rapidly that they are quite unmeasurable, it
is not impossible that the effect should be evident in
such a case as this, where the ionic concentrations
are so very small.

82. Effect of Acid Density on Capacity. — Measure-
ments of the capacity of a cell with varying acid
density, and with all the other factors which might
affect its behavior kept as constant as possible, give a
very simple and interesting result. The cell shows
its maximum of capacity for an acid of maximum

CAPACITY

187

conductivity. This is in both cases, for sulphuric acid,
of density about 1.22. (See Figure 53.) We shall
be better able to explain the reason for this coinci-
dence when we have discussed the facts about the

15*

ACID DENSITY

Fio. 53. — Change in cell capacity at various rates (1, 2, 4, 8, and 16
amperes) with various acid concentrations. (See also Figures 72
and 73).

internal resistance of our cell, and we will therefore
leave it until we reach that chapter (page 167).

83. Watt-hoar Capacity. — It is, of course, the
energy capacity, or watt-hour capacity, of the cell
which really interests us. This is found by multi-
plying the ampere-hour capacity by the average vol-
tage of discharge. The curves of Figure 54 are the
same as those of Figure 41, and on each a straight

138

STORAGE BATTERIES

line was laid out along the average cell electro-
motive force during the time of discharge. The
areas under these lines, including everything from
time zero to time-end of discharge, and from the
line of average electromotive force down to zero
electromotive force, give watt-hours if we multiply in

3 4 5 6

HOURS OF OlSCMARCt

Fia. 54. — Watt-hour capacity areas at various rates, and disoharge
curves from which they were taken. Discharge at 1, 1.4, 2, and 4
amperes.

each case by the discharge current. The rectangles
give the set of areas so produced, merely as visual in-
dication of the variation in energy capacity of a
storage cell with change in discharge current. The
same differences are given in Figure 55 for tempera-
ture variation, for one type of cell only. Other
curves for these same relations will be found on page

CAPACITY

139

253, in the discussion of yarious types of cells under
actual working conditions.

M. Weight Capacity. — For most purposes where
the battery has to be carried about the energy
capacity per pound of battery is a very important
ratio. This is especially true of batter-
ies which are used for electric vehicles,
and for submai*ine boats. The calcula-
tion of this factor is very simple. Divide
the total watt-hour output of
the battery at the desired rate
by the total weight of the
battery and con-
nections. Data on
actual tests will be
found in chapter
XVIII, page 254.

This factor is not
one of much interest

to the buyer of a large stationary battery, but it is a
matter of interest to the manufacturer who has to
pay for the lead used in making the battery, and
therefore has a good deal to do with the price which
he is obliged to ask for a battery to do a certain kind
of work. The modern tendency to install paste
plates in large emergency batteries is a good example
of this fact. The paste plates give a much larger
watt-hour efficiency per pound of total battery, and

Fio. 65. — Wattrhour capacity areas at
various temperatures.

140

STORAGE BATTERIES

as tbey are also much cheaper to make per killowatt-
hour, they can be sold cheaper tlian the large-surface
plates of the same total capacity. It becomes merely
a question of life and cost of maintenance whether
this type, or the perhaps longer-lived Plants plates,
shall be used for this work.

CHAPTER XI

EFFICIENCY

8& There are two ways of stating what is called
the effloiency of a storage cell. One of these is in
terms of ampere-hours; it is the ratio of the num-
ber of ampere-hours which can be taken out of the
cell to the number which must be put into it to bring
it back to its original condition. The other efficiency
is expressed in terms of watt-hours — the ratio of the
watt-hours taken out to those put in. The first kind of
efficiency is more or less misleading as a criterion of
the quality of a cell, but the second is of decided
interest and importance.

86. Ampere-hour Effloiency. — From what we have
already said about the behavior of a cell in charge
and discharge it is- evident that the ampere-hour
efficiency of most cells under the usual conditions
will be high — it will be nearly 100%. For the only
way in which current is lost is by local action and by
the evolution of gas during charge. If charge is
carried on at a very low rate, gas does not begin to
form on the plates until very near the end of charge.
The DE part of the charge curve (see Figure 27)

141

142 STORAGE BATTERIES

is steep and occupies only a small fraction of the
whole time. Gas begins to form rather suddenly,
and at this time the cell is practically fully charged.
Under these conditions the ratio

ampere-hours taken out
ampere-hours put in

is very nearly unity.

Even at fairly high rates the production of gas
only involves the expenditure of a comparatively
small fraction of the current sent into the cell, and
for working charge rates it leads to ampere-hour
efiSciencies of 90% to 95%.

The losses due to local action are very small if the
cell is charging and discharging with only a small
interval of rest. And this is usually the case where
efficiency is a factor of importance. If a battery is
standing on open circuit for a long time, with only
an occasional charge to keep it in good condition, and
with a rare discharge at a very high rate (as in the
case of a stand-by or emergency battery), efficiency as
such is not a factor which need be considered at all.
The interest on the battery investment on this latter
case is so much greater than all the coal expended
on it that the latter item disappears completely.
The factor which is of importance in such an emer-
gency battery is watt-hour capacity, and if this could
be attained conveniently with a cheap battery of

EFFICIENCY 148

efficiency 20%, we would see this type of battery
installed in stations which require this kind of ^^ in-
surance."

Formally, ampere-hour efficiency is

^charge 'charge

and for most purposes in service it will be found to
be from 90% to 95%. As far as this is concerned
the battery is about as efficient as any of the ordinary
electrical machinery.

87. Energy Efficiency. — The other and more im-
portant kind of efficiency is energy efficiency, and
this is the ratio of the energy which can be taken
from the cell to that put into it. Or,

jpip ^ watt-hours taken out
watt-hours put in

This is also evidently expressible as

where % and t have the same meaning as above and
Cc and Ba are the average cell voltages of charge and
discharge respectively.

88. Data for Efficiency Calculation. — The most direct
way to get data on the value of -E^ is for us to ex-
amine sets of curves like those in Figure 41 and
Figure 53 and calculate ampere- and watt-hour

144

8T0RA0E BATTERIES

4.0

2.0

1.4

1.0

Fio. 56. — Ampere-hour efficiencies at various rates. Plants plates
dischsirged at 1, 1.4, 2, and 4 amperes. Charge at 1 ampere.

efficiencies from them. Figures 56 and 57 gfive areas
so calculated from a similar set of charge and dis-

1.0

1.4

2.0

4.0

Fig. 67. — Watt-hour efficiencies at various rates. Plants plates dis-
charged at 1, 1.4, 2 and 4 amperes. Charge at same rate as dis-
charge.

EFFICIENCY

145

charge curves. It will be noticed that while the
ampere-hour efficiencies are good enough even at the
higher rates, the watt-hour efficiencies fall off pretty
rapidly, going as low as 60 % at the highest rates of
charge and discharge. These are rather extreme
cases, however, for storage cells in hard service are

1.0

1.4

2.0

4.0

Fio. 68.

rarely charged as fast as they are discharged, and the
actual figures are a little higher than those obtained
by holding rigorously to a charge rate as high as that
of discharge. This will be very evident if we take a
medium rate for charge and determine efficiency for
this rate and various discharge rates. Figure 58 gives
these data. Here we have assumed the one-hour rate
of charge, and taken the corresponding curve through-

s«&-

s — if

STOBAGB BATTBBIEa

out. At Tery low
rates the charge
and discharge vol-
tages may be nearly
the same through-
out the whole cycle
of operation. Fig-
ure 69 shows the
change in cell vol-
t^e at the various
low charge and dis-
roltagea charge rates given.
At the lowest rat«8
the cell shows an efficiency of nearly 100 ^.

Figure 60 shows charge and discharge voltage at
practical rates.

In batteries
which are worked
severely every day
and all day, at
rates which aver-
age perhaps as
high as the one-
hour rate of dis-
charge, the matter
of efficiency is """"""^

worth careful con- Fra- 60. — Average volUgea of chugBUid
.J .. TT J diecbarge at varioua practicAl rates.

sideration. Under piaotfi ceiii.

_,^^^ — > —

EFFICIENCY

147

these circumstances the difference in the coal bill for
an efficient and an inefficient battery may be of the
same order as tl^e depreciation and maintenance of
the battery for the same length of time. In vehicle
batteries which are worked on regular runs leading
to a full discharge every day or oftener, the same
relations will be found to hold. A difference of
10 % in watt-hour efficiency will be of the same im-
portance in dollars and cents as the depreciation on
the battery for the year. It is on such points as
this that choice must be made between two types of
battery. The battery with the slightly higher de-
preciation or shorter life is sometimes to be chosen
for the sake of the saving which can be made with it
on account of its higher watt-hour efficiency. We
can of course discuss matters of price and cost only
in the most general way, but we shall often have
occasion to call attention to points like this.

CHAPTER XII

INTERNAL RESISTANCE

89. Practical Cells. — The internal resistance of a
storage cell of commercial dimensions is very small
indeed and may frequently be entirely neglected in
calculations on the circuit containing a battery of
cells. Even in small portable cells the . resistance
seldom rises above 0.05 ohm and in large stationary
cells it may be as small as a few hundred-thousandths
of an ohm.

90. Specific Besistance. — In calculating and stating
the resistance of a substance we always take as refer-
ence a cube of the substance 1 cm. on an edge, with
electrodes covering the two opposite faces. This
specific resistance once known, we can calculate the
resistance of a wire of any size or length made from
the same material.

where K is the specific resistance, I is the length, and
q the area of the cross-section of the conductor, and
JB is the required resistance.

The table on page 263 gives the specific resistance

148

INTERNAL RESISTANCE

149

of some important substances. All pure metals have
positive temperature coefiScients — they increase their
resistance when they are heated. All electrolytes,
on the contrary, decrease in resistance with rise of
temperature. An alloy may behave in either way or

^ «

Ik
o

flO

10 » 90 40 SO 60

PtRCCNTAfiE OF Ht9\ IN SQLUnON

Fig. 61. — Specific resistance of sulphuric acid solutions containing

varying i)ercentages of 1.842 acid.

may have a positive coefficient at one temperature
and a negative one at another.

In the storage cell the solid substances all have
positive coefficients like metals. The electrolyte is
of course a member of the other class. The specific
resistance of sulphuric acid of various concentrations
is given in Figure 61.

For many calculations it is more convenient to

160 STORAGE BATTERIES

use the reciprocal of the resistance, the conductance,
and the corresponding specific conductance. The
conductance of electrolytes forms one of the most
interesting chapters of general eiectrochemistry, but
we shall not have occasion to use many of its prin-
ciples, and it must therefore be looked up in some
other book.

Unit conductance and unit resistance refer to the
same thing. A wire with resistance 100 ohms has
conductance 0.01, and so forth.

91. Acid Eesistance in the Cell. — Let us calculate
the approximate resistance of the electrolyte alone
in some cells of very different size. P^irst, a spark-
ing cell with three plates each 3 in. square
(7.6 X 7.6 cm.) and 0.4 in. apart (1 cm.). The
total acid area is

7.6 X 7.6 X 2 = 115 sq. cm.

The specific resistance of sulphuric acid of cell
strength is about 1.5, and since the plates are about
1 cm. apart, the resistance of the cell will be

1.5 XYi^ = 0.013 ohm.

The second calculation will be for a fairly large cell
such as would be used in a regulating battery. It
contains thirty-one plates, each 15 in. square and
with 0.4 in. separation. Tlie acid area is in this case

42 X 42 X 30 cm. = 17,000 sq. cm.,

INTERNAL RESISTANCE 151

and the acid resistance of the cell is

1.5 X

17,000'

or a little less than 0.0001 ohm.

About the largest cells which are in common use
have perhaps 131 plates about 15 x 30 in. In such
a cell the acid area is therefore about 290,000 sq. cm.
and the acid resistance is about 0.000005 ohm.

92. Aoid Resistance and Temperature. — The change
of resistance of the cell acid with temperature is
shown in the dotted curve of P^igure 62, and it is
also given quite accurately by an equation of the
form

i2, = JBo(l + «« + )8^)

where a and fi are calculated from measurements
made at two temperatures.

93. Acid Resistance and Cell Losses. — It may be
taken as an approximate general statement that the
total internal resistance of a cell is about double the
acid resistance. This approximation is usually suf-
ficiently close to be useful in the calculation of losses
inside the cell due to resistance.

Suppose we are drawing an average current of
2000 amperes from our biggest cell just considered.
The losses in the cell are

iV= 2000 X 2000 X 0.00001,

152

STORAGE BATTERIES

u
o

z
<
I-

ui
cr

A//

.06

.05

\
^

.03

v.
s

s
\
\
s

r 2

0* 3

0** 4(

)• 5

0* 60

TEMPeRATURE

Fio. 62. — Change in resiatance of cell add with temperature (dotted

line).

ISTEBNAL RSBI8TANCE

168

40 watts in aU. The cell ia furnishing 2000 x 1.8 =
3600 watts, and our resistance loss is therefore just
about 1%. This ia so small in comparison with the
normal working losses of the cell at this rate (about
25 9^) as to be negligible.

_&rj

1 '

■^

3?V

/■

rrz

i£-

TiuEDrascw(K«iNUNintQ
Fk). S3. — RcsiataDce curves of Plants cell during discharge at va-
rious temperatures.

94. Besistance Carvea. — It is quite true that the
internal resistance of a storage cell is usually negli-
gible as far as loss of energy is concerned. There
are, however, many things of great theoretical
(and therefore practical) interest about this factor.
Hardly anything about a lead cell gives so clear
an insight into its internal workings as its internal
Even its voltage curve cannot tell more

154

STOBAOE BATTERIES

about the minute phenomena of charge and dis-
charge than can be seen from its resistance carve.
Figure 63 gives a set of curves of resistance taken
during the disohai^e of a Plante cell at various tem-
peratures, and Figure 64 gives both voltage and

3
J

TME-UINUreS

resistance for the same cell at one temperature. It
will be noticed that the change in resistance is con-
siderable, if the cell is dischai^ed down below its
usual end voltage — say down nearly to zero. Fig-
ure 65 gives voltage and recovery curves during par-
tial discharge and recovery curves after open circuit
immediately following the dischai^e.

INTEBITAL RB8IBTA2TCE

155

9& Faoton of KetiitaiiM. — The total cell resistance
is evidently made up of at least three distinct
parts as indicated in the diagram of Figure 66: —

A. Support plate.

Ml \

—

th-

T/»£-/t/M/TES
Via, 65. — Curves of reoistaiice and voltage during discharEe and to-
coveiy. FlauU cell.

S. Active material, including electrolyte in the
pores.

O. Main body of electrolyte.

A and Ovfe can consider practically .constant, and
if changes, we can calculate the amount of the
change from the data of Figure 61, which gives the
relation between resistance and acid concentration.
B is the variable part of the system.

166

BTOSAQE BATTERIES

During oharge the active material first to react ie
near the surface of the plate, and the electrolyte does
not have to diffuse far through the narrow channels
of the mass. As the diffusion path increases and
the cell becomes more fuUy charged, concentrated
acid is produced in the pores. But all through the

Fia. 66. — Diagram of the parts of a PUnU cell.

charge it is the solid plate itself which does most of
the conducting, and the change of resistance to be
expected during charge is therefore not great.

During discharge a very different state of affairs
exists. In this case also the action begins at the
surface, where there is plenty of both electrolyte
and active material. But as discharge proceeds the
area of activity moves back deeper into the mass,
acid is used up within the plate and must be replaced
by diffusion. The acid concentration becomes much

INTERNAL RESISTANCE 157

lower at the point of activity, and there is added to
this the loss of conductivity by the solid plate itself.
The particles of lead and lead peroxide in the outer
layers have now become covered with a layer of lead
sulphate and have been more or less insulated from
each other. The result is as if the distance between
the plates had been increased, for the plate surface
which is actually carrying the current has moved
from the surface back into the interior of the plate.
The surface of the plate in contact with electrolyte
has also been greatly decreased by this displacement
of the active plate surface.

Such changes as these are quite sufficient to
account for the change found in the resistance of
cells under the usual conditions of charge and dis-
charge. We should not expect, and we do not find,
any very large or very rapid changes in cell resistance.

96. Sulphation. — On long standing, a storage cell
may acquire a very high resistance indeed as the re-
sult of complete ^^sulphation." This means that the
active lead sulphate formed during normal discharge
has gradually changed into the inactive crystalline
form, and that crystals of this inactive modification
have completely covered the particles of lead and
lead peroxide with an insulating coating. Authentic
cases are known of large cells with internal resist-
ance as high as 10 ohms.

As usual, it is hard to make things act properly

168 STORAGE BATTEBIE8

when you want them to. I have left a completely
discharged cell for six weeks or more, carefully fol-
lowing its internal resistance every day, and found no
change of more than a few per cent in its resistance.
It seems very likely that the ordinary cases of sul-
phation, which are rather common and most annoy-
ing in their results, do not lead so much to a very
high internal resistance as to poor contact between
particles of active material. The electrolyte can get
into the plate or the grid well enough, and the in-
ternal resistance of the cell can therefore not be
very high. But the capacity of the plate has suf-
fered because a good deal of what ought to be avail-
able active material has been incapsulated by sulphate
and removed from the reach of plate activities.

In ordinary practice, the cell is discharged only
until its electromotive force sinks to about 1.7 volts.
This means that only perhaps a quarter of the active
material of the plates has entered into reaction, and
that the increased resistance in the active mass is due
ratlier to separation of particles by sulphate coatings
than to complete transformation of the active mate-
rial at any place into insulating material. During
the charge, sulphate coatings and bridges are rapidly
broken down, and the decrease in resistance during
charge is therefore more rapid than could be explained
by a change in concentration of electrolyte within
the pores of the plate.

INTERNAL RESISTANCE 169

•

After a period of discharge, with corresponding
increase in resistance, the cell recovers its original
electromotive force along a curve nearly like a
diffusion curve when the circuit is opened. It also
recovers its original resistance along a very similar
curve. (See Figure 65.) This fact indicates the
dynamic nature of the equilibrium which causes the
cell to have any particular electromotive force or re-
sistance at a particular place in its discharge, charge,
or recovery curve. The particles of active material
cannot have been completely covered by insulating
sulphate, for on standing, the plate returns to its
original condition as far as we can measure it by an
examination of either electromotive force or resistance.

We must evidently think of the lead sulphate as
swelling up and almost plugging canals which lead
to unchanged lead and lead peroxide. The density
of the sulphate is much less than that of the materials
from which it is formed, and while the particles of
lead or peroxide may have had plenty of space be-
tween them at the end of charge, the sulphate must
shut off much of this from activity at anything like
a practical rate of discharge. As long as no current
is flowing, acid does make contact with the remanent
active material and the active plane in the plate
draws out toward the exterior.

In Figure 62 the full-line curve gives the open
circuit resistance of a small Plants cell at various

160 STORAGE BATTERIES

•

temperatures. The dotted curve shows only the
shape of the curve for the electrolyte, and not its true
value, which would be only about half that of the
cell at any point. The acid curve was plotted in this
way to show how the cell resistance departs from the
acid resistance at higher temperatures. Probably
the solid resistances of grid and active material be-
gin to make themselves felt, and as these have posi-
tive temperature coefficients, the increased resistance
makes the cell take a sharper turn than the elec-
trolyte. That the resistance of the plate material
becomes a factor is shown by the fact that pasted
plates of slightly greater area, placed as nearly as
possible the same distance apart, show a decidedly
greater resistance on open circuit than the Plante
plates. The cells with paste plates have about 25^
higher resistance.

97. Effect of Distribution of Material on Sesistanoe
Corves. — The curves of Figure 49 speak for them-
selves. The only queer thing about them is the flat
place which appears after 60 to 80 minutesof discharge.
This is characteristic of Plante plates with ribs, and
does not appear in the curves for paste plates. The
ribs of these plates are formed into active material,
which lies close to the ribs at their tops, but which
forms a solid mass down at the bottoms of the ribs.
(See Figure 67.) During the first part of the dis-
charge the electrolyte finds active material on the

INTSBNAL SBSI8TANCB 161

ribs, and diffusion takes place largely through the
open space between them, and only for a small dis>
tance through active material. As this easily avail-
able material is used up, the action moves farther
down into the plate and presently
reaches the mass of material at the '
bottom of the grooves. Here for
a time there is material enough at
a nearly constant distance from the
surface of the plate, and after this
has been passed the resistance rises
very rapidly and the plate poten-
tial shows that the cell is com-
pletely discharged.

If there is anj^hing in our fun-
damental theory of the dependence
of electromotive force on acid con-
centration, the curves of electro-
motive force of these cells ought Fm. 67.— Diagramoi

dJHtribution of active

to show a corresponding fiat place material oa ribbed
somewhere near the same point in "" '™"'
the discbai^e curve. The curves of Figure 52 show
it clearly except in the one for 8° C. We missed it
here by not taking points near enough together, for
it shows clearly in the curve of Figure 64, which was
made on the same cell at another time. This curve
gives the course of electromotive force and resistance
during a complete discharge followed by partial re-

162

8T0BA0E BATTEBIES

versal. If our explanation is correct, the resistance
ought to decrease very rapidly after passing through
a maximum at about the end of complete discharge.
The curve is in agreement with this idea.

TIME- MINUTES

FzQ. 68. — Change of internal resistance during discharge at vaiiouB

temperatures. Paste plates.

96. Paste plates show smooth curves of resistance,
as shown in Figure 68.

Our resistance curves should also be characteristic
when taken for dififerent rates, and Figure 69 shows
this for the same Plante plate cell at constant tem-
perature.

99. A most interesting idea of the lively dynamic

INTSBSAL RESISTANCE

163

nature of the momentary equilibrium existing in the
cell at any time during the cycle is obtained by
plotting curves of ooiutaiit oompoiitioa at various
times and temperatures. The curves of Figure 68

„

—

.'•

■^

—

-SmpB

i<a

IB discharge CBtcB.

are isothermal curves. Each one shows the course
of the change of resistance. during discharge at con-
stant rate and constant temperature. Since Fara-
day's law is true, the cell contains exactly tlie same
amount of lead, lead peroxide, lead sulphate, sul-
phuric acid, and water at the end of the same time
of discharge. Curves of constant corapositiou will

164

STORAGE BATTERIES

therefore result if we cut these isothermal curves at
times 30 min., 1 hr., 2 hr., etc., and plot the values
so found — resistance against temperature. Figure
70 shows a set of curves so found. The curve T=0
is for open circuit, and it gives the temperature

TOmMTWL

Fio. 70. — Resistance curves corresponding each to constant compooi-
tion of plates and electrolyte nuuie by cutting the curves of Figure
63 at various times.

[For example, after 60 minutes of discharge at 25*^ C, the cell had
a resistance of 0.06 ohm.]

resistance curve for the cell, like the full curve of
Figure 62, but on a different scale.

The slope of the curve T=s gives the tempera-
ture coefficient of resistance on open circuit at the
temperature corresponding to the point where the
slope is determined. The slope at any point on one

INTERNAL RESISTANCE 165

of the other curves is the temperature coefficient
corresponding to the temperature where the slope is
taken. For all the curves except ^ = the condi-
tion of the cell is one of momentary dynamic equilib-
rium. The materials are in the cell, without any
doubt, but their diftribntion depends to a great ex-
tent on the temperature at which discharge has
taken place.

100. Temperature Coeffloient during Activity. — The
open circuit temperature coefficient is about 1.5 %
per degree. The coefficient after 150 min. of dis-
charge is 23 % per degree. This latter value is of
course not like an ordinary temperature coefficient,
but it is most expressive of the lively nature of the
factors which determine the condition of a lead stor-
age cell at any moment in its life.

Corresponding curves for cell voltage are given in
Figure 71.

lOL Capacity and Acid Density. — At this point we
are prepared to examine the question left unanswered
on page 137. Why does the capacity of our cell
reach a maximum for acid of density about 1.22, as
appears from the measurements ?

The statement requires elaboration. It is not true
at all if the cell is examined at various working
rates, and if we measure merely the acid density in
the main body of the cell. It may very well be the
truth, if we take into account the dilution of the

166

STORAGE BATTERIES

acid ii> the pores of the active material, and if we
base our calculation on the density of acid inside
the plate.

The curves of Figure 53 show how the capacity of
the cell changes with the acid concentration in the

10* 30*

TEMPERATURE

50*

Fio. 71. — Voltage curves corresponding to constant composition of
plates and electrolyte.

[For example, after 60 minutes of discharge at 25*^ C, the cell showed
a voltage of 1.69.]

electrolyte. This particular set of curves was made
with paste plates, and corresponding curves for large
surface Plante plates would show some difference
in shape and would have their maxima at other
points. But it is very evident in every case that
the maximum of capacity shifts toward the region of
higher acid density as the rate is raised. Rate must
evidently be taken into account in making any state-

INTERNAL BE8ISTANCS

167

ment about the relation between capacity and acid
density. This becomes still more evident if we
examine into the change of capacity of positive and
negative plates separately. Figure 72 gives data
for the positive plate and Figure 73 for the negative.

■ ■

""^

10*

15*

20* 25*

ACID DENSITY

ao»

3S^

Fio. 72. — Change in capacity with variation of acid density. At dis-
charge rates of 1, 2, 4, and 8 amperes. Paste positive plates,
measured against auxiliary electrode.

It is evident that as far as the positive plate is
concerned we must go up to a very high value of
acid density to reach the maximum of capacity,
while for negatives at ordinary rates we need only
acid of ordinary density to bring us out to the maxi-
mum. For the positive we should have acid of

168

STORAGE BATTEBIjBS

density 1.32 and higher. For the negative we need
only to go as far as 1.2, which is well within the
range of practical operation. The facts have some-
what the appearance of contradicting the explana-

>
I-

n-N.

-^ ■

■"^

10*

15*

20* Z5'

ACID DCNsmr

zor

FiQ. 73. — Change in capacity with variation in acid density at va-
rious rates. Negatives.

tion which Dolazalek gives for the appearance of
this maximum. He says : —

" At the beginning of discharge the current lines
enter only the outer layers of the active material,
where they find the least resistance. As the change
in concentration develops polarization in the outer
layers, the current lines penetrate deeper and deeper
into the plate, and these lines have density such that

INTERNAL BE8I8TANCE 169

everywhere in the pores the drop in potential (fr) is
equal to the polarization prevailing in the outer
layers. This condition must of necessity be ful-
filled, for the active material, lead as well as lead
peroxide, is a good conductor, and the potential must
therefore be the same in the pores and out near the
surface of the plate. If the polarization in the outer
layers has reached 0.2 volt, the potential of the
whole accumulator has also fallen by the same
amount, and this would be the point at which dis-
charge would be stopped. At this time the current
lines have penetrated so far into the active material
that the drop of potential in the pores — the product
of current and pore resistance (ir) — has also reached
the value 0.2 volt.

" But the resistance of the pores is determined by
the conductivity of the acid which fills them. The
better the acid conducts, the later the moment will
appear when the product (ir) reaches the value 0.2
volt, and therefore the greater the capacity of the
cell. The conductivity of sulphuric solution increases
at first with increase of concentration, reaches a
maximum at 30% of H2SO4, and then decreases
again. The above discussion shows that the capacity
must also reach its maximum for 30% acid, and this
is splendidly confirmed by the measurements."

As a matter of fact, it is quite evident from the
curves that the measurements do not confirm this

170 STOBAOE BATTEBIEB

•

conclusion at all, if we confine our measurement of
acid density to reading a hydrometer placed in the
cell electrolyte between the plates. But if we con-
sider at the same time the difference between the
density of the acid in the pores and that in the main
body of the electrolyte, — this same difference which
we have already had occasion to mention so often, —
Dolazalek's hypothesis fits much better.

102. The Concentration of the Active Ion. — The
ion which really determines the electromotive force
at the cathode (the peroxide plate during discharge)
is H^, and the current is driving this ion toward the
peroxide, 2 H+ for each SO^ sent in the opposite
direction, and five times more rapidly as well, because
of its greater migration velocity. The reaction at
this electrode requires 4 H^ for each PbO^, and 2 H^O
is formed as the result of the reaction. Besides the
lowering of acid density due to the formation and
precipitation of PbSO^, we are diluting our elec-
trolyte by the addition of 2 H^O. Acid of maximum
conductivity is about 1 of H^SO^ to 19 of H^O,
and it may very well be possible that the acid con-
centration out in the cell is much higher than it is in
the pores at the place where the reaction is taking
place.

At the negative plate (the lead plate) things are
not so bad. Here SO^ is the determining ion, and
it is used up in the pores to form PbSO^, more being

INTERNAL BE8I8TANCE

171

sent along as an ion by the current. Here we do not
have the formation of water to dilute the acid at the
point of reaction, and in spite of the fact that the
SO4 moves much more slowly than H"*", there is less
change of density inside the plate. A smaller excess
density in the main body of the electrolyte is sufficient
to maintain the concentration at the point of action.

CHAPTER XIII

PHYSICAL CHARACTERISTICS

103. So far we have been considering the chemical
processes in the cell and the behavior of the elements
of the cell under varying conditions. We have not
paid much attention to the physical nature of the
plates and we have been judging them by their
works rather than by their looks. It is interesting
to examine the plates of our cell somewhat more
closely — they sometimes give a good deal of valu-
able information.

Most of the hard battery service is done by plates
of the Plants type. This name does not now mean
the lead sheets used by the inventor, but indicates
that the active material of the positive plate has been
formed from metallic lead and not from a paste of
lead salts. For the hard service into which these
plates are called certain fundamental properties are
necessary. Most important of all is the power to
deliver current at a high rate with a reasonable
efficiency. A reasonable life must also be given
under these service conditions.

The type is a comparatively simple one. It may

172

PHYSICAL CHARACTERISTICS 173

be represented diagrammatically by Figure 66. Its
special characteristics are : —

Large surface.

Active material near conducting plate and elec-
trolyte.

Reserve of metallic lead for further formation in
service.

A certain minimum of mechanical strength.

A new positive plate of this type should have just
enough peroxide on it to give its rated capacity,
without much to spare. This peroxide has been
formed in the factory under the most favorable con-
ditions, and it may even contain a little cement sul-
phate from its rapid formation. If it goes into good
hard service, it probably loses a full quarter of this
original peroxide in a few months. Whatever there
was on the plate that was at all loose or liable to be-
come so, has been knocked off by the rapid evolution
of gas during charge. By this time the original
material, whatever its nature may have been, has
been replaced by a firmly adherent and dense layer
of peroxide which hugs close to the lead of the plate.
Ribs, rosettes, and pores have opened to better diffu-
sion of the electrolyte, and the plate with its rather
" skimpy" but readily accessible peroxide layer, is in
the pink of condition for hard work. Its capacity at
the high rate at which it is working is perhaps even
increased, in spite of the fact that it has lost a good

174 STORAGE BATTERIES

quarter of the active material with which it started
to work and has probably regained but a very small
fraction of the loss.

If this same positive plate has gone into slow and
easy service, it will also change, though not so much
in external appearance, after a few months of service.
Its ribs or rosettes will become filled with peroxide,
and it will increase in total capacity. Too low a
charge rate is liable to crowd the spaces in the plate
and produce buckling or twisting.

In either case the plate seems to adapt itself as
well as it can to existing conditions — to its "envi-
ronment." It increases its capacity at the rate at
which it is called upon to work. If now the high
and low rate plates were to be interchanged, the one
going into easy service instead of hard, and vice ver8a^
there might be trouble for a while. The " skimpy "
skin formation, which was just what was needed at
the high rate, will not give the low rate capacity
which the other plate has been easily delivering.
And the low rate plate will nearly explode when it is
first put on at the high rate. It throws off excess
active material for a time and as remanent sulphate,
always present in a plate worked at very low rates,
is cleared away, action on the support plate itself may
be severe for a time. Buckling or stretching may
appear. If the plate passes this danger point safely,
it settles down to the high rate pace and becomes

PHYSICAL CHABACTERISTICS 175

before very long much like its predecessor. In the
meantime the former high rater, which made so poor
a showing during its first few cycles at the low rate,
has picked up gradually. More material forms from
the reserve lead under the low charge rate, and most
of this remains in the plate. Gradually the capacity
rises until it is quite sufficient for the work, and by
this time the two plates have completely interchanged
their natures and looks. It seems to be generally
true that a plate that has been working at high rates
is in no special danger when put on easier work. The
reverse is not true by any means. It is a ticklish
operation to break in a plate for high rate work
which has been in operation for a long time in very
easy service.

104. Densities. — If we examine the densities and
the relative volumes occupied by lead, lead sulphate,
and lead peroxide, it is immediately evident that
shrinking and expansion are sure to occur during
charge and discharge. The following table gives
the data: —

DENSITIES

Metallic Lead 11.4

Peroxide, hydra ted 7.4

Peroxide, dry 9.4

Lead Sulphate 6.2

Litharge 9.3

Redl^ad 8.9

176 STORAGE BATTERIES

A good many pretty mysterious occurrences in
battery practice should be referred directly to these
differences of density. For instance, most Plante
plates, during the process of making them from pure
lead, grow in length. Some of those with long ver-
tical ribs without many breaks in them may grow an
inch in length per foot of plate. There is every rea-
son to believe that this stretching is caused wholly
by the crowding of sulphate as it is formed from
lead. A properly forming plate has its sulphate in
the form of a very dense and firmly coherent layer,
and as this is formed from the soft lead of the ribs
it hangs to them and crowds. The cumulative effect
is proportional to the length of unbroken rib along
which the crowding takes place, and the stretching
is proportional to this factor also. It is also very
different for various forming agents, probably be-
cause the coherence of the sulphate to the lead of
the plate is different for each.

It will be noticed from the table of densities that
the peroxide layer which is finally formed on the
positive as the result of formation is denser than the
sulphate from which it came. So the properly formed
Plante plate has a peroxide layer with just about the
right degree of porosity. If it« active material were
more porous, it would be at the expense of coherence ;
and if it were denser, diffusion would be poor, and
the plate would give low capacity at high rates.

PHYSICAL CHARACTERISTICS 177

Metallic lead is the densest of the materials in the
table, and negative plates, which are to be porous,
too, if they are to have reasonably good capacity,
must be made to have very large and highly devel-
oped surfaces. This can be more or less successfully
attained in the case of Plante plates by the natural
method of forming them. True Plante negative
plates are always made by formation first as perox-
ide, by attack of a forming agent and action of the
current on the pure lead of the grid. They are sub-
sequently completely reversed to sponge lead and
are then finished negatives. The surface is, of
course, enormously increased by the formation of
grains of peroxide from the solid lead, and when the
reversal is given to the negative condition, sponge
lead is formed right where the grains of peroxide
were. Since its density is greater, it only partially
fills the space occupied by the particle of peroxide or
sulphate, and as a matter of fact it is more like a
mere slender network when the plate is finished than
like the dense solid from which it came.

Paste plates make natural negatives. Litharge
and red lead are dense compared with sulphate, and
if the paste plate is allowed to sulphate as completely
as possible before formation and is then reduced to
lead, the resulting sponge has passed through the
state of lead sulphate, with its greater volume, and
has then gone on to become metallic lead, shrinking

178

STORAGE BATTERIES

all the time during this latter change, and opening
pores everywhere during the final change.

The extremely small solubility of lead peroxide
probably accounts for the fact that it is always pres-
ent in fine grains, which never grow to any size, even
after many cycles of service. It cannot stay in solu-
tion long enough to move about and look for a place
to settle where there is already a crystal of peroxide.
Lead sulphate is comparatively soluble, and when
metallic lead is formed from it, the lead ion has a
chance to look for a nucleus of lead on which to
precipitate. The result is that negative plates in-
crease in average size of grain with service, and finally
show a much decreased capacity as compared with
their original one. Not because there is less lead in
the plate, but because the available surface has be-
come smaller.

CHAPTER XIV

FORMATION OF PLANTS PLATES

lOS. In the early days of lead storage cells, forma-
tion was a very slow and expensive process, requiring
a month or more for its completion and the expendi-
ture of a great deal of primary battery material. For
at that time the primary cells were the only source
of current for the purpose, and primary cells have
never been very cheap as a source of power. The
plates of those early batteries were really plates of
lead, either quite flat or with slight corrugations
which enabled them to hold a little more active
material on the roughened surfaces. These plates
were set up in their final cell positions in dilute sul-
phuric acid, usually in acid much more dilute than
we now use for the purpose. The cells were then
subjected to a series of reversals — they were charged
first in one direction and then in the other.

When the acid is poured into the cells, thin layers
of lead sulphate form on both plates, and this process
ceases as soon as the layer has become thick enough
to protect the plate from further action. Charge is
begun in either direction, as the plates are just alike

179

180 STORAGE BATTERIES

and there is no reason to decide, at this point, which
plate is eventually to become peroxide and which is
to become sponge lead. Under the action of the
current the lead sulphate layer at the anode is
changed into peroxide and that at the cathode is
changed to sponge lead. The thin peroxide layer is
then a complete protection against further action and
the other plate is cathode, and needs no protection.
As soon as charge has been carried this far, the cell
becomes a gas generator and nothing more. All the
current is used to produce hydrogen at the cathode
and oxygen at the anode.

The capacity of such a cell is very small indeed.
It will give a spark if it is short-circuited, but not
much more. For the amouot of lead sulphate which
is formed before a lead plate protects itself against
further action by the acid is minute, and no more
sponge lead can be formed at the negative than cor-
responds to the original quantity of sulphate on it.
At the peroxide plate there will be action on the lead
of the plate and formation of somewhat more sulphate
than was originally present, but this action takes
place only during a part of the charge, and before
long the dense peroxide layer shuts off the lead plate
completely from further attack.

If now the cell be immediately put on charge in
the opposite direction, the results are not good. The
active material formed during the first charge turns

FORMATION OF PLANTE PLATES 181

over very quickly and the plates reverse their po-
larity, but only a little more active material is pro-
duced. It took Plants only a short time to find out
that much better results were obtained by letting the
cell stand discharged before each reversal. After
standing at rest, discharged, for a day or so, the cell
is reversed. Not much is gained in the way of
capacity this time, but when the cell is again reversed
it is found that considerable gain has been made.
Local action, especially at the peroxide plate, has re-
sulted in deeper attack on the lead, and subsequent
reversals and periods of rest give finally an active
material layer of useful thickness. The two plates
look different after they have been formed. There
is a layer of brown peroxide on one and a layer of
gray sponge lead on the other. ^

If the capacity was forced too far by more forma-
tion, the peroxide layer was liable to slough off and
fall to the bottom of the cell. To be sure, more was
formed to take its place, but the battery has reached
its maximum capacity and further formation was
merely a waste of current — an expensive article in
those days.

This was during the first stage in development.
Before long it was found that ribs and in general
mechanical development of the surface of the lead
plates permitted of much more formation and so
gave higher capacity. Then before long came the

182 STORAGE BATTERIES

idea of rapid formation — the use of chemical agents
to aid and hasten the electrolysis, and along these
lines the modern " rapid forming processes " gradu-
ally came into use. There are many points about
the older process which are interesting and which
lead directly to an explanation of the theory of the
later methods of formation.

The first point to be remembered is that lead sul-
phate does not form a dense enough layer on lead to
protect it from the action of an electric current in
sulphuric acid. A plate is quite protected by such
a layer, provided no current is passing, but it has no
power to resist the more active attack of the anion,
backed by the driving force of the current.

The second point is that a connected layer of
peroxide does protect against attack, even when the
plate is anode and current is passing through the
cell. The other point to be kept in mind is that
the positive plate can discharge itself by "local
action " while it is at rest. In the case of the Plante
plate, with its thin coating of active material, this
self-discharge may be pretty nearly a complete one
in the time of rest recommended for Plante formation.

The curve of Figure 74 shows how rapidly this
action takes place in the case of a plate which has
been subjected to only a few Plants cycles, and which
has therefore a very thin layer of peroxide on its sur-
face.

FORXATIOy OF PLANTE PLATBB

183

It U the most natural thing in the world that such
a plate should discharge itself on standing, for it is
really a whole storage cell. Lead plate, peroxide
plate, sulphuric acid, all are present in every per-
oxide plate, and tlte surface of contact is very large
in proportion to the mass of peroxide. It discbarges
during its period
of rest wherever
lead and peroxide
are in contact, and
lead sulphate ia
formed at these
points. During
the subsequent
reversal all tlie ma-
terial on the per-
oxide plate ia con-
verted into sponge f,q. 74.
lead, and this in-
cludes new sulphate formed from the plate itself as a
result of the local action following the previous per-
oxidation. During the rest now taking place after
reversal local action is increasing the sulphate con-
tent of the other (peroxide) plat«, and so on.

The pertinent query arises : Why does not every
peroxide plate discharge itself by local action ? It
does, but only to the same extent that the older
Plante plate would. Where lead and lead peroxide

i 1

s „

'■ «

i r

i ^^

' J ' ' '— 10 1 --H i » M

- Sclf-diacharge of origiDal FlantA

184 STORAGE BATTERIES

are in contact every positive plate discharges itself,
but the amount of material in contact in a modern
plate is so small in proportion to the total amount
of active material in the plate that the amount of
action on the plate is comparatively small, and only
a low percentage of the total capacity of the cell is
lost through the effect. The action is, however,
strictly proportional to the surface of contact be-
tween lead and peroxide, and the modern high-rate
plates are subject to much greater losses from this
cause than are the paste plates. Fortunately the
efficient large surface plate does its important work
under conditions of rapid reversal — discharge and
charge follow each other very rapidly, and the cell
is never standing at rest for more than a few min-
utes at a time.

106. Modem << Bapid Plante " Formation. — After
the first excitement over Plante's discovery had
passed, it was not very long before the small ca-
pacity of the flat plates was felt to be a drawback.
The surface was increased by corrugating or other-
wise roughening it. At this same time the original
method of forming by a series of reversals began to
seem slow and wasteful of current. So methods
were sought which should permit of attaining the
same or better results more easily and rapidly, and
these methods were : —

1. To begin the attack on the lead by treating the

FORMATION OF PLANTS PLATES 185

plate with an etching agent, nitric acid, for example,
which dissolves some of the lead and roughens the
surface of the plate. This treatment was followed
by regular Plants formation, but the process went
on much more rapidly than in the original method.

2. To produce on the surface of the lead plate
some compound which could afterward be changed
into peroxide by a single charge. One of these ideas
was to subject the plate to the action of sulphur.
Lead sulphide was formed, and this was changed first
into sulphate and then to peroxide during the period
of charge.

3. To add to the sulphuric acid used in formation
an agent which should attack and dissolve the lead
of the plate. This resulted in formation, first of a
soluble lead salt, then of sulphate by reaction with
the sulphuric acid of the electrolyte, and finally of
peroxide by the usual effect of the current.

This last method is the usual one nowadays, and
the great majority of all Plant6 plates are now
formed from lead plates by electrolysis in a sulphuric
acid solution containing a "forming agent." The
most efficient method of applying this principle seems
to be to use as agent a substance which can furnish
an anion capable of forming a soluble lead salt.

The common soluble lead salts are : the nitrate,
acetate (chloride), chlorate, perchlorate, and sulphite,
and these are (or have been) all used for the purpose.

186

8T0SA0B BATTSBISa

It is not our bueiness to examine technical recipes
or to study the minutiaa of manufacturing processes.
But we can state a general theory of formation which
will be found applicable to all the different processes.
107. Tlieory of Sapid
Formation. — Figure 75
givea a diagrammatic
picture of the different
zones and stages in the
formatiou of a lead plate.
All plates are formed into
peroxide first, if they fall
into this class at all, even
if they are eventually to
become negatives; so thia
one picture covers all the
cases.

The solution contains
sulphuric acid and the
forming agent, which has
as anion an ion which can
yield a soluble salt of
lead. The charging cur-
rent started, this forming ion and SO^ migrate
toward the plate. The velocity of the forming ion
may apparently be either greater or less than that of
the SOj ion without making any difference in the
process. At any rate, we will suppose that the two

-DQ^

^lOM

FORMATION OF PLANTjf PLATES 187

ions reach the plate at the same time. A layer of
soluble lead salt in solution is formed at once, but
this lasts only an instant. SO4 is there and lead
sulphate is immediately precipitated. The regular
charging reaction then comes into play and the sul-
phate is transformed into peroxide. In the mean-
time the forming ion has been freed, and it bores into
the plate again to form more soluble material, which
is precipitated by SO^ , and so on.

This insures formation, but the relative concen-
trations of the two active ions must be carefully
balanced if it is to proceed far enough to make it a
practical success. If there is too little forming ion
in proportion to the sulphate ion, sulphate will pre-
cipitate as a dense layer clinging closely to the plate,
and peroxidation follows so closely that the plate
soon protects itself. If there is too much forming
ion relative to the SO^ — ion, an actual layer of solu-
tion, containing a considerable concentration of the
soluble lead salt, forms between the plate and the
layer of precipitated sulphate. The sulphate layer
is thus kept from close contact with the plate at all
points, and when peroxide forms, the whole sheet of
active material, partly sulphate and partly peroxide,
is so loosely attached that it flakes off at the least
provocation, leaving the plate bare.

The formation of a tough and coherent peroxide
demands careful attention to the relative concentra-

188 BTORAOE BATTERIES

tions of the active ions. It may be taken as a general
rule that there is no one acid concentration and no
one forming ion concentration that produce correct
formation. For each acid concentration there will
be, however, an optimum concentration of the form-
ing ion, and other considerations usually make it
advisable to use a rather low acid concentration for
the forming solution.

Formation to a practical depth usually requires
eight or ten times the number of ampere-hours after-
ward to be required of the plate in service. This is
quite natural, for as we have seen in Chapter X, we
use in service only about 10 to 30 % of the total
active material of the plate. If the plate is an old-
fashioned thin-layered flat Plante plate, the maximum
proportion of the total will be brought into use. If
it is a modern plate with ribs or rosettes, a smaller
part of the total peroxide will be turned over in
practice.

108. Low Voltage Formation. — A special mode of
formation has been invented and patented by PoUak,
and while it has apparently not been adopted as a
manufacturing method, it is of interest as an example
of a principle we have frequently applied. Lead
sulphate cannot protect a lead plate from attack
when current is passing and the plate is anode. If
we can prevent the formation of lead peroxide and
continue to form sulphate, there is no reason why

FORMATION OF PL ANTE^ PLATES 189

formation without any special agent should not be
carried as far as we choose.

Peroxide is not formed from sulphate except at
cell voltages higher than 2 volts. If therefore we
send current through the cell at a voltage slightly
lower than this value, only sulphate will result, and
the plate will continue to be attacked. This con-
dition of things is best attained by connecting the
lead blank which is to be formed to a fully charged
peroxide plate of capacity sufficient to complete for-
mation. This means a charged peroxide plate of
eight or ten times the caj^acity desired for the
finished plate we are making. When enough sul-
phate has been produced to give final capacity, the
sulphate-formed plate is taken out of this cell and
formed to peroxide in another cell, either against
negative plates or flat lead dummies. In the mean-
time the auxiliary forming positives are receiving a
new charge to get them ready for the next forma-
tion. There seem to be practical reasons why this
idea has not been generally adopted. Theoretically
and as a laboratory experiment it works quite per-
fectly.

109. Changes in the Forming Agent daring Forma-
tion. — It is much to be desired that the activity of
the forming agent should cease as soon as the plate
is brought up to its proper capacity. If some of
this dangerous substance remains in the plate, it will

190 BT0BA6E BATTERIES

continue its original behavior and attack the lead
of the peroxide plate during each period of charge.
Of course this attack is much weakened by the fact
that the plate is completely peroxidized and also be-
cause it is never discharged to such an extent that
much of the peroxide in contact with the lead sup-
port is changed to sulphate. But a lead cell must
have a life of several years and must go through a
great many cycles of charge and discharge, and even
a small amount of action can be cumulatively harm-
ful.

Some of the forming agents mentioned in the list
are only too ready to eliminate themselves. When
chlorine ion is used either as hydrochloric acid or as
a chloride, chlorine gas is evolved nearly quantita-
tively at the anode, and the forming agent must be
replaced accordingly. Chlorates are also broken up
with evolution of chlorine, but not so completely as
CI" ion. Nitric acid is reduced at the cathode, first
to nitrous acid and finally to ammonium sulphate.
This necessitates renewal during formation and final
saturation of the electrolyte with ammonium sul-
phate. This means that small quantities of nitric
acid, left in a plate as the result of formation, are
perfectly eliminated from the cell during its first
few cycles of active operation.

An interesting suggestion is that of Beckmann.
Sulphur dioxide in water solution forms some sul-

FORMATION OF PLANTS PLATES 191

phurous acid, HjSOg, and this gives a forming ion
SOg — , because lead sulphite is a fairly soluble sub-
stance.

During formation this ion leads the attack on the
lead plate as described, but it is itself oxidized rather
readily to SO^ , and so a few cycles are sufficient
to remove completely every trace of extraneous ion
from the cell. This also seems rather difficult to
apply as a practical forming process, as SO2 is not a
pleasant substance to have about in large quantities.

Acetate ion, CjHgOj"", is most persistent and can
cause great damage if any of it is left in the plate
after formation. Even this is gradually destroyed
as the result of cell activity.

Perchlorate ion, ClO^", is apparently the only sub-
stance in the list which is perfectly resistant to the
effects of the current. It is therefore the most effec-
tive of all forming agents, as it does not need to be
renewed at all in tlie forming tanks. For this same
reason it might become a dangerous factor in the
cell after it goes into service. Fortunately the
limits of proportion between which perchlorate ion
can act as a forming ion in sulphuric acid solution
are narrow. In electrolyte the sulphuric acid con-
centration is comparatively high, and the little rem-
nant of perchlorate is therefore a very small fraction
indeed. Under these conditions it hardly has any
power of attacking lead, and while in proper propor-

192 STORAGE BATTERIES

tions it is perhaps the most active of all forming re-
agents, it is much less dangerous than many of the
others in the conditions of ordinary service.

Ua Plants Negativeg. — The negative Plante plate
is made in exactly the same way as the positive. It
is formed as a positive, with the aid of a rapid form-
ing agent, and is then reversed completely, so that all
the peroxide is changed to sponge lead under the
action of the current.

Such a plate has all the good qualities of the large
surface positive, especially during the first part of its
life. It is easily reached by the electrolyte and can
give large discharges without danger. Later in its
life it loses a considerable part of its original capacity
because of increase in size of grain and loss of
porosity. It must therefore be made to have a much
larger original excess capacity than the positive,
which increases its capacity by local action and slow
formation in service. Most Plant6 negatives are
made to give nearly 100 % excess capacity when they
go into service. This excess is rather rapidly lost
during the first six months or so of service, and at
the end of the first year the plate will usually show
an excess of only about 25%.

The curves of Figure 76 show how light Plante
positives and negatives change in capacity in service.
The curves are of course only averages, and differ-
ent types would show somewhat different curves, but

FORMATION OF PLANTS PLATES

198

these can safely be taken as representing the gen-
eral course of events.

Many makers use pasted negatives entirely, even
in batteries which are to be called on for the hardest

110

100

-s^

\ ■

jjl

NUMBER OF CYCLES

Fio. 76. — Change in capacity in hard service. Light Plants plates.

service. Their life is sufficient, and their excess
capacity is so great that no fear need be entertained
that the negatives will ever limit the discharge of the
cell.

CHAPTER XV

PASTS PLATES

It was Faure who first conceived the idea of
producing active materials for accumulator plates by
the electrolysis of lead compounds instead of from
the lead of the plate itself, and he began the evolu-
tion of what are called paste plates. Faure probably
reasoned somewhat like this: Plant6 produces lead
sponge and lead peroxide by a wearisome and ex-
pensive attack on the solid lead. It would certainly
be much better to cover a lead plate with a mass
which can then be easily and completely converted
into lead at the cathode and lead peroxide at the
anode, and such a plate can be made to have capacity
enormously greater than the thin-skinned plates of
Plante. Some triumphs and not a few troubles for
many people began just at this point in the history
of galvanic cells. As we now know very well, Faure's
invention was not able to push Plante's out of the
field. Each of the two types of plate has a perfectly
definite place and service of its own, and while the
two types appear to cross into each other's territory
now and then, there is always some very definite
reason for the apparent intrusion.

19i

PASTE PLATES 195

•

The process of making a paste plate is a very
simple one. Perhaps the people who find most
difficulty in the process are the ones who have to
actually manufacture the plates for the market. The
difficulties are all practical ones and so minute and
difficult to sort out and describe and remedy that we
can only hope to touch the more evident and funda-
mental ones.

Suppose it is desired to make a set of fairly light
plates to be used in an electric automobile. They
must have good capacity per unit
of weight, mechanical strength
sufficient to withstand the jar of
road service, and a fairly long life ^^'^^T^^^^^^^^
(say 250 to 300 cycles), if they
are to compete with other plates already on the mar-
ket. We will make the positive plates first.

For positives, a grid which can hold the peroxide
in place somewhat is usually considered best. Lead
peroxide has very little coherence and drops off the
plate surface very easily unless it is kept in some way
from doing so. We should therefore choose a grid
of the general form shown in Figure 77, having ribs
with inward dovetails to keep the material in the
plate. It is usual to cast the grids of 6 to 10 % anti-
mony alloy. This gives a much stiffer grid than
pure lead and prevents attack by the acid of the
electrolyte. Molds we will assume — they are not

196 STORAGE BATTERIES

within the province of our discussion — and we will
also assume that we have a supply of grids ready
cast. The next thing is to paste them.

Recipes for positive pastes are legion. A very
simple one which can be made to give good results is
made by mixing litharge (PbO), or red lead (PbjO^),
or a mixture of the two, with rather dilute sulphuric
acid. A paste is made of the constituents, just
thick enough to permit of its being worked into
the holes and hollows of the grid. If then a plate
so pasted is set in the air, it dries and at the same
time sulphates, setting to a hard mass. ' Better re-
sults are obtained by soaking the freshly pasted plate
in dilute sulphuric acid for several days. During
this time what is perhaps the most important thing
in the whole life of the plate takes place. It cements.

Lead peroxide is a powdery, non-coherent mass at
best, and a plate pasted with pure peroxide has very
little mechanical strength compared with the plat^
which has been treated in the way just described.
But lead sulphate, crystallizing into a firm, connected
mass all through the interstices between the grains of
oxide and peroxide, can become a most useful bind-
ing material. Just a word about what we mean -by
the general term cement.

A cement sticks things together. It does this by
first of all penetrating, as a liquid, all the irregu-
lar holes and crannies and spaces between the solid

PASTE PLATES 197

particles to be held together. It then afterward
hardens to a solid and fills all these irregular spaces,
thus dovetailing the various pieces of the whole mass
into a single piece. The resulting solid is as strong
as its two final constituents — one of them the original
solid which was to be bound together, the other the
new solid formed by the hardening of the cement.

If red lead is used in the paste, the following reac-
tion takes place partially as soon as the acid used in
mixing has a chance to react : —

PbgO^ + 2 HaSO^ = 2 PbSO^ + PbO^ + 2 H^O.

The plate therefore contains lead peroxide, red lead,
and lead sulphate, as soon as it has set and before
formation is begun. If litharge alone has been used
in the paste, the unformed plate contains only lead
oxide and lead sulphate. The lead sulphate reacts
quickly, and within a few minutes or at most a few
hours after the plate has been placed in the cement-
ing acid bath, the sulphation of the plate is quan-
titatively complete. But the second and equally
important step — the locking together of the plate
by the sulphate — takes place much more slowly. It
depends on the recrystallization of lead sulphate and
is an action very like the dreaded "sulphation" which
is so often the cause of trouble in the vehicle batteries
all over the country. The fine particles of sulphate are
more soluble than the larger ones, and the latter grow

198 STORAGE BATTERIES

at the expense of the smaller ones. As the crystals
grow they interlace and lock themselves together, as
growing masses of crystals always do. One sul-
phate crystal, growing out from between grains of
oxide or peroxide, touches the one growing out from
the neighboring opening and the two coalesce. The
result of this crystalline growth and interlocking is
the cementing of the plate. It becomes hard, sounds
hard when it is struck, can be used as a hammer and
pounded on the floor without losing any paste ex-
cept at the place where the lead grid is actually bent
or broken. It is now ready to be formed.

112. Formation of Paste Positives. — The plate, des-
tined to become a positive, is now hung in a bath of
rather dilute sulphuric acid and made the anode for
the passage of the forming current for perhaps 60
hours. Figure 78 shows the changes which take place
in its composition during this time. At the start
the plate contained : —

PbO 55 %
PbO^ 25%
PbSO^ 20 %

The lead oxide begins to turn to peroxide right
away as soon as charge is begun, but the sulphate
content of the plate rises for several hours. This
may be because the plate is becoming more porous
as formation proceeds, so that the acid finds unused

PASTE PLATES

199

oxide ready to hand as it enters new channels. But
before long the sulphate also passes over into peroxide

240 tao

60 120 160 too

AMPERE-HOURS FORM/VTION

Fio. 78. — Changes in composition of a paste positive during formation.

and at the end of the period of formation the active
material consists of : —

PbO 9 %
PbOj, 88%
PbSO^ 3%

Our cement is nearly gone. But even this 3%
is a potent factor in the life of this, positive plate,
and if formation has been carried on at the right
current density, there is also some cementing, or
rather loose interlocking, of the particles of peroxide.

It seems probable that this remanent lead sulphate

200 STORAGE BATTERIES

is never removed from the plate under proper condi-
tions of charge and discharge and that it forms a net-
work which really helps to hold the peroxide together.
During each discharge sulphate is deposited on this
nucleus, and the plate may perhaps be partially held
together by the binding action so produced during
the succeeding period of charge, which is so trying
to the paste plate.

Surel)'^ this cannot be the whole story of the making
of a paste positive ? There are hundreds of secrets
carefully guarded, and hundreds of patents and reci-
pes for pastes. A glance at the patent literature
shows the nature of the various things that might be
added to the positive paste — alcohols and organic
acids, salts and sugars, and almost anything else that
one could think of. The intention of these additions
is to aid in producing either one of two desirable
things : —

(a) An increase in the hardness of the plate, and
therefore increased life.

(6) An increase in porosity, and therefore its
eflBciency.

The organic acids — carbolic acid, for example
— hasten the cementing action. Probably a lead
phenolate or some such substance is formed and lead
sulphate is then rapidly produced from this. The
soluble lead salt would naturally hasten sulphation
just as a forming agent hastened it in the case of

PASTE PLATES 201

Plants plates. The addition to the paste of a soluble
salt like magnesium sulphate has not much effect
unless the plate is allowed to dry after pasting and
before formation. The salt crystallizes all through
the plate while it is dr)'ing and setting, and is then
dissolved again during formation, leaving spaces in
the formed active material and thus increasing po-
rosity. A good many manufacturers probably still
feel the need of a " hardening agent " or a " porosity
agent," or both. But it seems perfectly possible to
get along without either of them. And perhaps the
final result is just about as satisfactory if only lead
oxide and sulphuric acid are used instead of the more
mysterious and cabalistic formulee of some of the in-
ventors in this field. It is, as a matter of fact, very
hard to see how any good effect of the addition of
any of these agents to the paste can remain after the
resulting plate has been through fifty cycles of hard
work. Long before that time the hardening agent
has been completely decomposed and removed from
the cell so completely that chemical analysis will
often fail to show a trace of it. The porosity agent
is of course dissolved out and diluted through the
cell as a part of its activity. The active material of
the plate has been turned over and over and has dis-
posed itself in new ways — filling up the old pores
and channels and making new ones for itself. All
that is left is a very small trace of lead oxide and the

202 STORAGE BATTERIES

normal proportion of lead peroxide and lead sulphate.
Whatever coherence the paste now has is due to these
two substances, and as we have already seen, lead
peroxide is not inclined to bind together to give
much mechanical strength. The remanent network
of sulphate is all that holds the plate together.
Whenever particles of peroxide lose contact at the
surface of the plate their fate is to fall off sooner or
later and collect in the bottom of the containing jar.
The cementing sulphate has no chance to persist at
the surface. It is transformed almost completely
into peroxide at each charge. So the peroxide plate
naturally loses active material by " shedding," and
the rapid evolution of gas which accompanies the end
of each charge helps to throw off all the loose par-
ticles. It is the fate of all paste positives, even the
most healthy, to finally become a mere skeleton — a
grid — with nothing left on it but a few bunches of
peroxide clinging to its ribs.

113. Paste Eecipes. — Every manufacturer has his
own particular recipe for positive paste. This and
other facts lead to the conclusion that the propor-
tions are not of great importance. Many manufac-
turers make good plates, and they use —

1. Pure litharge.

2. Pure red lead.

3. Mixtures of litharge and red lead in all propor-
tions.

PASTE PLATES 203

Some makers mix their paste with strong sul-
phuric acid ; some use it weak. Evidently there is
much in knowing how to paste, dry, cement, and
form — much more than in any secret of proportions
or materials.

This statement might almost be taken as an axiom
in battery manufacture.

114. Paste Vegatives. — The finished negative paste
plate has a ver}*^ different set of characteristics and a
very different life history from its weaker positive
brother, but it begins in very much the same way.
Since it is to become spongy metallic lead, it may as
well be made of litharge unless there is some special
reason against this, for the step from PbO to Pb is
the easiest possible one and takes less energy than
the one from Pb804 or PbOj to Pb. No hardening
agent is needed, for the negative has plenty of co-
herence. But it does need porosity, and a good
many makers use either a soluble salt like magne-
sium sulphate, or an inert substance like graphite,
in making their negative paste. It seems doubtful
whether the effect of the soluble salt is lasting, and
there seems to be a belief that graphite and the other
space-filling inert substances which are suggested
may be harmful in the ordinary open-grid negative
plate. So we will make our negatives as simply as
possible, using only litharge and rather dilute sul-
phuric acid, and allowing the plate to set and cement

204

STOBAQE BATTEBISa

very much as though it were to become a positive.
It sulphates to the amount of about 30 fe of the
whole mass, and during formation the changes shown
in Figure 79 take place. In this case the plate was
about 20 % sulphate before formation, and 80 ^

5^:::

AMPtRE-tKMIS FOMkTKM
Fia. 70. — Changu in composition in a paste negative plate during

litharge. I^ad begins to form immediately when
the current is started, but notice how the sulphate
content also rises during this period — almost as fast
as lead is formed. Tlie pores are opening. Metallic
lead occupies much less space t)ian either the oxide
or the sulphate, and the acid has a chance to reach
and attack new oxide in the deeper porea of the
plate. Before long the sulphate reaches its maxi-

PASTE PLATES 205

mum, and then it seems to reduce faster than it is
formed from the oxide. Finally the plate stops
when it contains about 98% of metallic lead, the
rest being mainly oxide, with a very small remnant
of sulphate.

Lead sponge made in this way is tough, coherent,
and well interlocked all over the plate, and a
properly made negative has a chance of much longer
life than the positive made in about
the same way. It is usually said
that one set of negatives will just
about outlast two sets of positives, ^^pa^'^gatim. ^^
The rites of negative grids are
often made with dovetails as shown in Figure 80, the
intention being to hold the contracting material in
better contact with the support.

115. "Chloride " and " Box " Negatives. — Two vari-
ants on the usual processes have been of importance.
The " chloride " negative was made by casting a lead
grid around pellets made from molten lead chloride.
The whole plate was then reduced to sponge lead,
and the active material so formed had many good
qualities. This process is no longer in use. The
other plate in this class is the " box " negative, origi-
nated by the most important of the German battery
companies and now used in this country by the
Electric Storage Battery Company. The appear-
ance of the finished plate is shown in Figure 91.

206

8T0BA0E BATTERIES

Pellets containing litharge mixed with some lamp-
black or other " expander " are made outside of the
plate and dropped into place in the openings. They
are then covered by the other sheet of perforated
lead, and the plate is complete. This particular
active material has no coherence at all, and would
fall out of the openings in an ordinary grid in a few
days of service, but by protecting it with this per-
forated cover it can be made to give good capacity
and life.

(CHAPTER XVI

DISEASES AND TROUBLES

11& Frequent mention has been made of action
between the peroxide and the lead support in the
positive plate, resulting in self-discharge proportional
to the quantity of material affected. Lead sulphate
is formed at the surface of contact. This action is a
perfectly normal part of the activity of every positive
plate. It is a large factor for the original flat plates
of Plante, fairly large — quite measurable at any
rate — for modern large surface plates, very small in
paste plates.

While this action is a normal one, and essential
in its nature, it may be so exaggerated by wrong
operating conditions that it becomes a source of
danger.

Between sponge lead and solid lead the difference
of potential is so small that self-discharge is very
slight. But in many of the modern negative plates
there are other things than lead. Many have graphite
in them to give contact, insure porosity, and make
the active material a better conductor. With this
substance in the negative material there is a good

207

208 STORAGE BATTERIES

deal of local action, and the negatives may discharge
themselves quite as fast as the positives in the same
cell.

These normal effects of self-discharge we must
take with our storage cell, for they are a part of its
nature. There are many other substances which
might be in the cell — impurities — and which can
greatly increase the local action. Some of these are
so strong in their eflfects that they are dangerous to
the life of the cell.

Suppose, for example, that a very stable and per-
sistent forming agent has been used in the manufac-
ture of the plate and that this has not been carefully
removed after formation and before the plate is put
into service. During each charging period this
forming agent will bore into the peroxide plate
(anode) and continue formation at a rate determined
by the concentration of the forming ion. From our
discussion of rapid formation it will be remembered
that maximum rapidity of formation, and density
and coherence of material formed, result from using
a definite value for the ratio —

concentration of forming agent
concentration of acid

and that the velocity of formation dropped very
rapidly when the concentration of forming ion was
carried much below the value indicated by this ratio*

^
\

■w

DISEASES AND TROUBLES 209

In the working cell there is not much likelihood of
enough of our stable and persistent forming agent
remaining in the plate to approach this value. If
such an agent were present at anything like the
optimum concentration, the positive plate would
have a total life of only a few cycles. By that time
the lead support would be completely peroxidized,
and the plate would fall to pieces.

Large surface plates attain a life of 1000 or more
discharges. If a plate is to compete on these terms,
even a minute amount of forming action makes a
difference in results, and so manufacturers have
learned to carefully remove the forming agent before
sending their plates into service.

Another thing helps very much. Most active
forming agents are soon completely decomposed by
the electrochemical action of the cell. Nitric acid
has been frequently used as an active forming agent.
It is reduced to ammonia at the cathode and remains
in the cell only as a slight impurity of ammonium
sulphate in the electrolyte. While this latter sub-
stance is not to be prescribed as good for the cell it is
not actively dangerous.

This danger is confined to the peroxide plate,
and the most unhealthy impurities are the forming
agents of the list given on page 185. Of course the
dangerous ions turn and go to the negative (lead
sponge) plate during discharge, but the voltage is

210 STORAGE BATTERIES

much lower and the plate appears well able to pro-
tect itself by a layer of sulphate.

117. The lead sponge plate has its own class of
uncomfortable impurities — the metals — and they
have no power to affect the life of the plate. They
merely cause self-discharge. This they do by set-
tling on the plate and causing little local cells.
During charge the lead plate is cathode. All the
metallic ions in the cell wander over to this plate,
and if they can go out of solution at the voltage
of charge and under the existing conditions in the
cell, they deposit as metal on the lead plate. Little
cells

metal/sulphuric acid/lead

discharge as soon as the voltage is removed, and
the current used in their discharge is lost as far as
external work is concerned. The cell appears on
test to have lost capacity.

Evidently the noble metals will be the chief of-
fenders, for they go out of solution very readily and
give a local cell with a good big electromotive force
for self-discharge. A very little platinum will keep
a negative plate from taking in more than a minute
fraction of its proper charge. This unpleasant effect
does not persist for many cycles ; for while the noble
metals are ready enough to go out of solution, they
are not ready to go back in again. At any rate,

DISEASES AND TROUBLES 211

when the lead plate is cathode (charge) the noble
metal goes out before the lead does, and the latter
plates it over and eventually covers it away out of
reach. As the negative naturally increases the size
of its grain in service, the noble metals are gradually
incapsulated in the heart of the lead grains, which
no longer react completely to the very center at each
reversal.

Copper, silver, and gold can act in the same way as
platinum. Copper is not very active, and the ac-
tivity increases to the other end of the list.

lis. There is still a third class of impurities which
can cause self-discharge, though its representatives
have no direct effect on the plates. This class in-
cludes those ions which can exist in two stages of
oxidation and which are easily converted from one
state to the other. Iron is the commonest example.
Suppose a workman drops a pair of pliers into a
storage cell during its installation. When the elec-
trolyte is poured into the cell, these pliers dissolve
gradually to form ferrous sulphate, and now the cell
contains Fe"'"''" ferrous ion. This travels about in the
cell, and during discharge it migrates along with the
H"*" to the cathode, now the peroxide plate. When
it meets with lead peroxide, it is oxidized to Fe^"'"'*'
ferric ion. Even if the cell is on open circuit, the
action will take place as fast as Fe"*""*" reaches the
peroxide plate, and as soon as a little Fe"^"^ has been

212 STORAGE BATTERIES

oxidized to Fe"^"'"'" a slight concentration gradient is
set up which hastens the motion of Fe"*""^ toward the
peroxide plate and the removal of Fe"^^"*" from the
neighborhood. In the meantime Fe**"^"*" has wan-
dered over to the lead plate, and there it is reduced
to Fe"^"^, setting up a diffusion gradient there in the
same direction as the one at the other plate. Every-
thing conspires to aid in the discharge so produced.
No metallic iron is deposited, but every bit of Fe"*"*"
and Fe"^"^"*" in the cell keeps busily at work running
from one plate to the other and discharging the cell.
Even a small amount of pliers in a large cell will
cause a considerable self-discharge in 24 hr. This
is, of course, an effect which is especially noticeable
on open circuit. If the cell is working hard, charg-
ing and discharging every few hours or every few
minutes, the loss of energy will be negligible.

Probable Xmpurities. — The list includes: —

Forming agent. From rapid forming process.

Iron.

Copper.

Tin.

Arsenic.

Antimony.

Platinum (noble metals in general).

119. A certain amount of depreciation must be
expected in a battery, even if it is kept in the best
possible condition. The effects of local action cannot

DISEASES AND TROUBLES 213

be avoided, nor can the negative active material re-
tain its original porous structure throughout the
whole life of the cell. Plates shed their active ma-
terial. Positive peroxide loses its coherence and falls
off the plate even in the case of the toughest of Plante
type, and to a much greater extent in paste types.

These normal disturbances may be greatly magni-
fied by poor operating conditions. We will make a
list of the common diseases which are especially ap-
parent in Plants types.

1. Loss of capacity, — This is due to wholly differ-
ent causes in positive and negative plates. A Plante
positive should retain its capacity almost unchanged
up to nearly the end of its life. It has great power
of recuperation and can re-form lost active material
and should remain healthy for the rate at which it is
operating if it is carefully handled. Toward the end
of its life all the reserve lead will become exhausted.
If it is made with rosettes, like the Manchester type,
all the pure lead in the strips becomes changed into
peroxide, and the plate then becomes like a rather
low-surface paste plate. The grid remains unat-
tacked, but the capacity has reached a maximum,
and from this time on peroxide will be shed and no
more can be formed to replace it. Events follow
much the same course in a ribbed Plants plate. The
ribs will become entirely peroxidized and the main
supporting webs have not sufficient surface to keep

214 STORAGE BATTERIES

up the supply. The ribs finally disappear, as do the
rosettes of the Manchester type. The plate is ap-
proaching the end of its useful life.

120. The Plante negative has a more peaceful ex-
istence and an almost indefinite life, but it diminishes
rather rapidly in capacity during the first hundred
cycles or so of service and continues to lose more and
more unless it is regenerated by some means. This
loss of capacity has been spoken of before (page 192).
It is due to the increase in size of grain and the
general decrease in surface which results from many
cycles of charge and discharge. The large grains
persist and are not completely transformed into sul-
phate during discharge. The lead deposits on them
rather than to form new grains. Then, too, the
smaller grains are more soluble than the large ones,
and these two effects taken together combine to pro-
duce a continual and considerable droop in capacity
with service. One way to bring, back the original
condition of the plate is to completely reverse it to
peroxide and then back to lead again, but this is not
very frequently feasible in practice, where the plate
is set up with many other positives and negatives in
a large cell.

121. Another way of restoring the original capacity
of a Plants negative is by means of a process called
" Permanizing. " The plate is soaked in a rather
strong solution of sugar and then heated to about

DISEASES AND TROUBLES 215

300° C. for a time. The sugar is quite completely
carbonized at a point below the melting point of lead,
and the pores of the active material are filled with
very finely divided carbon. This carbon prevents
the pores from filling up with lead, and the grains
may also act as centers on which lead can precipitate.
At any rate, plates treated in this way seem to retain
their capacity longer than usual, and a plate which
has lost a part of its capacity by service has most of
it restored by the treatment.

2. Deformation. — All Plante plates are more or
less subject to buckling or fracture. If they are
made of pure lead, they twist and stretch when any
strain is put on them, and if they are made of anti-
mony alloy, they are liable to crack instead. In the
case of pure lead plates, buckling may be caused
by improper formation. If one side of the plate is
formed more deeply or completely than the other, the
changes of volume which occur will twist or bend the
soft lead and the plate buckles. Almost all Plante
plates with ribs grow in length considerably during
formation, and if the resulting peroxide is dense and
firmly attached to the lead of the support, the
stretching may be as much as an inch or more. It
is almost wholly along the rib — much less marked
across the plate ; a perfectly normal effect, and known
and allowed for by all manufacturers who make this
type of plate. Lead is so soft a metal that the

216 STORAGE BATTERIES

material produced, which is greater in volume than
the lead from which it is made, and which adheres
strongly to the surface, exerts force sufficient to
stretch the whole plate.

Certain operating conditions may tend to cause
buckling. For example, if a battery has been on
very high rate work, its ribs and pores are very open.
If now it is changed over and put on low rates, espe-
cially of charge, its plates are very liable to buckle.
Much new peroxide will be formed away down near
the central support of the plate, and this can easily
fill the available space between ribs too full.

And sulphation, in the evil sense of the word, can
cause plates to tie themselves almost into knots.
Here the change of volume is as great as possible,
and all the pores and spaces in the plate are over-
crowded with material. It may be taken as a gen-
eral rule that any treatment which can cause more
than the normal change of volume in the deeper
active material of the plate will give rise to buckling
or fracture.

3. Sulphation, — This is a " waste-basket word "
among all the people who have to deal with storage
batteries. Whenever anything whatever seems
wrong with a cell, the first diagnosis is "sulphated."
Lead sulphate usually has something to do with the
difficulty, but its connection may be of the most re-
mote. The most common cause of trouble is lack of

DISEASES AND TROUBLES 217

proper charge. In days not so long past, batteries
were often sent out a long way into the country, to
a point miles distant from the power house, and
allowed to " float " on a trolley line to help the vol-
tage and save copper feeders. These lonely batteries
often had a hard time as far as proper charge was
concerned, and some of them furnished examples of
sulphation and buckling of the most aggravated
nature. Engineering practice has improved since
then, and boosters and feeders have been found eco-
nomical compared with the rapid depreciation of
batteries used in this way. In the case of station
batteries properly operated, there is not nowadays
much cause to use the word "sulphation."

4. Impurities and local discharge. — Before the
danger of very low charging rates and the worse
danger arising from a net discharge were clearly
appreciated, many of the troubles with plates were
sought for in the presence of "impurities" in the
cells. Every rapid forming agent was suspected,
and water, acid, and even air were examined with
great care for possible explanations of trouble. It
will be evident from what has been said about the
elimination of the forming agent and its comparative
action in very dilute solution that these analyses and
examinations were without positive result. A stor-
age cell should contain nothing but sulphuric acid;
but it takes a long time to accumulate troublesome

218 STORAOE BATTERIES

impurities if reasonably pure water is used to fill the
cells, and many of the troubles mentioned appeared
within a few months of service. It seems now fairly
certain that the whole effect could be explained by
undercharge, by the fact that the plates got a net
discharge, and by the fact that the charging rates
were much too low. Certainly these factors can
cause sulphation and buckling, and even destruction
of a whole battery, in the way these troubles used to
occur.

5. Shedding of active materiaL — Plante positives
shed. So do paste plates, but the shedding is a more
healthy thing for the Plante plate, and is a part of
its physiology. On page 174 there was pictured the
way in which well-made Plante plates adapt them-
selves to the rate at which they are working. No
plate can do this so well as the simple ribbed type of
positive. Even the Manchester plate, nearly uni-
versal in its application though it may be, cannot
compete with the simple ribbed pure lead type in
adaptability, and especially in lively response to the
demands of very rapid rates. At low and inter-
mediate rates the sensitive pure lead plate is at a
disadvantage, for it is endangered by low charge
rates, and is by no means so excellent at low dis-
charge rates as at high ones.

Plante negatives have none of these weaknesses.
Their only failing is the one already described —

DISEASES AND TROUBLES 219

rapid loss of capacity. As far as health and tough-
ness are concerned, they are beyond criticism.

6. Short circuits in the cell. — The almost universal
use of wood separators has nearly removed this once
common source of trouble. Any large surface plate
develops strips and flakes of surface sulphate or other
surface material. This drops off and sometimes
reaches across from positive plate to neighboring
negative. Often these delicate bridges are quite
innocuous, but they occasionally become formed part
way or all the way across, and the result is a complete
short circuit in the cell. Local action may be very
great indeed at the two points of contact of this
bridge, and many a plate has had a hole eaten right
through it by the very high local current within a
few days after the accident occurred. Rigorous in-
spection is the only way to avoid such an accident,
and the acid density is the very best indicator of
trouble. In small glass jars it is easy to see whether
anything has occurred, but in the big lead-lined tanks
used for large batteries it would be a great deal of
work to look down between each of the ten thousand
or more pairs of plates every day. If the cell is not
working properly, its acid density will not rise during
charge to the proper value, and this may always be
considered a sign of trouble.

As a battery grows old much sediment forms in
the bottom of the cells, and if this is not removed,

220 STORAGE BATTERIES

the plates will eventually short-circuit across their
bottom edges. Pure carelessness or laziness only can
account for such a condition.

7. General debility. — The " storage battery man "
learns to judge pretty well about the condition of a
battery by looking it over. " She don't look fight,"
is reason for a careful investigation. If a battery
has been doing well a^nd then begins to show signs of
ill health, an examination of the charge and discharge
charts will usually show the reason for the change.
Perhaps the station has been called on for heavier
loads during a period of two weeks or so. A prime
power unit may have been out of commission in the
station. The old booster may not be large enough
for the work to be done. It usually turns out that
the battery has given a net discharge, or else the
necessary net overcharge cannot be given in the
time that remains after the hard work of the day.
Some such cause will usually be found.

122. A few years ago I had hundreds of plates
sent to me for chemical analysis from batteries where
troubles of this kind appeared. The plates and the
electrolyte were in all cases as pure as possible, but
in most cases investigation showed that the battery
was being charged at too low a rate and not fully
charged at that ; the plates had buckled and turned
in color. In every case where investigation was pos-
sible operating conditions were responsible, but it

DISEASES AND TROUBLES 221

sometimes took careful examination and even diplo*-
macy to bring out this truth. A good starting point
in cases like this is the maxim ^^ Look at the rates
under which the battery is working." If a compara-
tively new battery, once healthy and lively, turns
weak and sickly, and plates begin to buckle and shed,
do not suspect " impurities." Suspect operating con-
ditions. See that the battery is charged. See that
it is overcharged, and the chances are large that all
the troubles will disappear.

These directions are sometimes overdone, but not
very often in my experience. It is, of course, quite
possible to overcharge Plante plates until almost all
the active material is blown off the positive plates
by continued gassing. But few superintendents will
allow their battery men to waste current in this way.
Oftener they are obliged to beg for enough charging
current to keep the battery in good condition.

A well-made large surface plate seems to love
work. No battery looks so healthy (to me at least)
as one which has stripped itself for service, at, say,
the 20-min. rate or better. The plates look lean,
but their color is good. They do not gas very much
except at the very end of charge. The current which
can be drawn from such a battery, especially when
it is installed in a warm place, is astonishing. In
earlier days the 8-lir. rate was "normal." In pres-
ent-day service the 6-min. rate is more nearly the

222 STORAGE BATTERIES

rate at which the battery is most useful. There is a
good reason for this. Suppose our battery can give
100 amperes for 8 hr. So can a 10 KW. 110-volt
generator. This battery can give 3000 amperes for
a minute or so. It would take fifteen or twenty
generators to safely handle such a peak.

123. After the catalogue of ills just recited it
might seem that the lead battery must be given up
as a bad job. But we have been acting in the role
of tlie pathologist in this case, and as a matter of
fact the lead cell is a pretty healthy and lively
machine, if it is well treated. Even under rather
adverse conditions it often shows surprising powers
of resistance. In our own laboratory we have cells in
use which are over twelve years old. This battery has
had occasional periods of a few months each of hard
service, with long rests between. The rests have
probably been harder on the plates than the work,
for it has sometimes been left pretty well discharged,
and the results have shown themselves in disintegra-
tion of the negative plates.

In easy service the life of positive plates should cer-
tainly reach six years, and that of negatives is much
longer. In stand-by service positives may last ten
years and negatives twelve or fifteen. In hard regu-
lation work the positive life is three to five years and
negative life five to eight.

Paste plates in service are much shorter lived.

DISEASES AND TROUBLES 223

Probably about 300 to 350 cycles for the positives
and about 400 to 600 for the negatives may be
taken as the average life. In stand-by service there
seems to be no reason why the life should not be
nearly as long as for Plante plates. Local action is
much less effective, and the battery is kept well
charged.

124. It is possible to give some general rules for
the operation of batteries. For Plant6 plates : —

1. Keep the battery charged.

2. Charge at a fairly high rate. Usually this
means at the 8-hr. rate or a little higher.

3. Inspect frequently and remove all possible
short circuits immediately.

4. Keep acid density at the proper point.

5. Keep the acid above the top of the plates.

6. If plates buckle, straighten them as soon as
possible.

7. Do not let the temperature reach too high a
point. (100° F. is a safe limit.)

Discharge at almost any rate does not harm good
Plante plates provided they are charged immediately
after the discharge is finished.

For paste plates : —

1. Charge at a low rate, 12 hr. or lower.

2. Overcharge occasionally by 10 % or so. Once
a week is often enough for the overcharge if the
battery is in daily service.

224

STORAGE BATTERIES

3. Use an ampere-hour meter and regulate charge
and discharge by that.

4. Try to give a nearly complete discharge be-
fore recharging. If the discharge is extended over
two or three days, no harm is done.

6. Watch temperature carefully. High tempera-
ture is much more destructive to paste plates than
to Plante types.

6. Test each cell frequently and inspect at the
least sign of trouble.

The most usual trouble arises from continued net
undercharge, especially in private installations.

CHAPTER XVII

SOME COMMERCIAL TYPES

The most important services performed by
storage batteries are in regulation of large station
loads and as " stand-by " batteries. The work per-
formed in these two applications is wholly different,
and there is a very evident movement toward the use
of quite different types of plates in the two kinds of
service.

Eegolation (Trolley Service, Large Factory Service,
etc.). — The battery is used in conjunction with a
large power plant and often with a "booster." The
charge and discharge rate vary from five minutes to
twenty seconds or so. This is the hardest and most
wearing service that a battery can be called on to
perform, and it is the most important from the point
of view of economy. High service Plante plates are
eminently fitted for the work, and paste plates are
quite out of their element.

A very large number of patents have been taken

out on plates of the Plante type, and most of them

have dealt with the methods of increasing the surface

of the plate or with the method of forming it. Not

Q 225

BTORAQE BATTEBtSa

many of the really marked variations have met with
commercial succesBi and gradually practice has left

only a very few really fundamental Flante plate
types.

The fundamental intention is to increase the active
surface of the plate by forming ribs. This develop-
ment of the surface is carried out before formation
j^_ with a rapid forming agent.

" ^S^^ r~> The Tudor plate may be

- ^^ -^ taken as type (Figures 80

and 81), It is made by cast-
ing pure lead in a mold of
proper shape, and is prob-
ably the best known and
most generally used of all
European plates.

Other means than casting
are also used to produce

SOME COMMEBCIAL TTPE8 227

the same increase of surface. The Gould plate
(Figures 83 aDil 84) is made from pure sheet lead

Fia. 83. — Section and

by a process of " spinning. " The sheet of lead is fed
back and forth between rapidly rotating mandrels

Fia. 84. — Stepfl in the apinoioB o( a " Gould " plate.

filled with steel disks spaced far enough apart to give
the right strength of rib for any particular service.

8T0BAQE BATTBRim

The National plate (Figure 86) looks much like the
Tudor, but is made by iVB^ing ribs and webs from a
sheet of pure lead instead of by
casting. Other plates very simi-
lar in final appear-
ance are made by
plowing, by pressing
sheet lead through a
die under great pres-
sure, and in various
other ways.

One of the varia-
tions, and one of the
oldest and most gen-
erally used, is the " Manchester " posi-
tive, shown in Figure 87 and already
frequently mentioned in the more the-
oretical part of this book. This is, not
a very high surface plate, but it has
shown itself well fitted for almost every
kind of work. As
will be seen from
the cut, the active
material is formed
from " rosettes " of
lead ribbou, and
these are pressed into a cast frame of antimony lead
before formation. The frame is so stiff that buck-

SOME COMMERCIAL TYPES 229

ling should not take place except under extreme ill
treatment, and the surfiice is sufficient
for any except the very highest rates. It
is perhaps not quite so efficient at high
rates as tlie plates with larger developed

J surface (Tudor,

I Gould, National),

^ but the latter de-

mand rather more
: care in operation.
! The Gould plate
« (Figure 88) has
f the longest rihs
° of any of the
■i types and its sur- Fio. 87. — ■■MaQcbestet"

1 face is very large

^ in j»roportion to its area. This is with-

1 out question the plate most responsive

■I in high-rate work, and most efficient in

■3 the liardest service, but the greater sur-

* face and longer rib mean greater inher-

j. ent danger from local action and greater

. probability of buckling unless operating
£ conditions are closely watched.

It is perfectly feasible to operate any
of these high-surface batteries at aston-
ishing rates, and in modern installations
it is usually the booster which limits the

230 STORAGE BATTBBIB8

battery discharge. Most manufacturers are quite
willing to send their batteries out to work at the
5-min. or even the 1-min. rate of discharge. A
glance at the table will show what sort of an " over-
load " this is, if the term has any application to a
storage battery.

" Normal rate " 1 for 8 hr.

X 2for3hr.

X 4 for 1 hr.

X 8 for 20 min.

X 16 for 5 min.

X 32 for 1 min.
Of course the term "normal" as applied to the
8-hr. rate has lost significance, since the most im-
portant work of the battery is nowadays performed
at a very much higher rate, and batteries of large
size are not often put in for service at this rate ex-
cept for stand-by or insurance purposes. The 20-
min. rate is more nearly " normal " in modern battery
practice.

In regulation work, batteries are usually operated
in conjunction with a large power plant. The cells
have each seventy-five to a hundred plates about
15 X 31 in., or 18 x 18 in. (See Figure 89.) Each
15 X 31 in. positive plate gives 40 amperes for 8 hr.,
and from this the capacity of the battery at various
rates can easily be calculated. Suppose each cell has
101 plates.

80UB COMMEBCIAL TTPB8 231

50 positives x 40 = 2000 amperes for 8 hr.

or 4000 amperes for 8 hr.

or 8000 amperes for 1 hr.

or 16,000 amperes for 20 min.

or 32,000 amperes for 5 min.
If the battery is working in conjunction with a
500-volt power circuit, it will consist of about 260

Fia. S9. — One cell of a large regulatiiiB battery.
cells. The power obtainable from the battery is
therefore

2000 amperes at 500 volts =

1000 KW. for 8 hr.
and from this on up to
32,000 amperes at about 400 volts =

12,000 KW. for 5 min.

232 STORAGE BATTERIES

Such a battery would only be used in connection
with a very large power plant — say of 5000 KW.
or more.

It will be quite evident how such a battery should
be used. Its little 1000 KW. would hardly be felt
at the 8-hr. rate, but its 12,000 KW. can give reg-
ulation of enormous short peaks. For momentary
peaks, lasting only a fraction of a minute at their
maximum, this battery could furnish up to 25,000
KW.

As a matter of fact the total quantity of energy
furnished by a single discharge of this battery is not
very large, as measured by modern requirements.
It can give

1000x8 =8000KW.H.
if discharged at the 8-hr. rate, and

12,000 x^ =1000 KW.H.

if discharged at the 5-min. rate.

Its main importance lies in its power to absorb
and give up very large quantities of energy in very
short times without danger to itself or trouble to any
one about the station.

^^ Stand-by '' or Insurance Batteries. — The most im-
portant of all the applications of the storage battery
is, strange to say, the one in which it is called upon to
do the least actual work. This is as a mere reserve of
power, to be used only in case of emergency.

234 STORAGE BATTERIES

It is of the utmost importance that the supply of
light and power, in a city or in any large service,
should be continuous. The central power stations
of a city supply thousands of consumers in every
possible application of electric power. Lights, heat,
machinery of every description, elevators, — all de-
pend on the continuous service given by the power
company. Any accident which resulted in stopping
the supply of energy, even for a few minutes, would
do a lot of damage and inconvenience many people.
The stopping of all the generators in one of the New
York stations would leave thousands of people in the
dark, without elevator service, with no work to do
because all the machinery in the factory was dead.

The great supply companies, like the various
Edison Companies of the country, take every pre-
caution to prevent such a stoppage in service. En-
gines, turbines, generators, — all are installed in
separate units, each of which has only a fraction of
the work of the station. Enough extra sets are pro-
vided to allow for all necessary repairs and replace-
ments without interruption of service. At the
bottom of all these precautions, the power house has
connected with it a huge storage battery, which is
kept constantly charged and which is called on for
active service only in case of the utmost need.

The engineer in charge of the station has taken
every precaution and has provided for every possible

SOME COMMERCIAL TYPES 235

emergency. But if anything should happen which
puts the power house out of action for a time, the
battery is big enough to carry the whole station
load for a few minutes — long enough to get aid
from neighboring stations or to make rapid repairs
and changes. The battery is the only source of
power which is wholly reliable. There are no mov-
ing parts, and there are no )iigh pressures to cause
trouble.

One of these stand-by batteries may cost 8200,000
and be called on for only two or three real discharges
a year. Interest and depreciation is perliaps $25,000
a year, and so these discharges cost $12,000 apiece, —
a couple of dollars per kilowatt-hour; but quite
worth the price, for the station was able to continue
uninterrupted service. The battery pays for itself
in " good will " alone.

For this particular class of service the manufac-
turers are beginning to use a new class of plate. As
far as life and capacity under high rate is concerned,
the large surface Plants plate is of course the best,
and many stand-by batteries of this type are in use.
But they are expensive to make. Local action is
considerable, and this may be especially true at the
very low charging rate at which it is often necessary
to charge such a battery. Paste plates can do this
work quite as well as the more expensive Plante bat-
tery. They hold a charge longer, and work best on low

236 STORAGE BATTERIES

charge rates. The life of a paste plate battery is
quite sufficient and its efficiency is good.

Figure 90 shows a large stand-by battery of paste
plates. The experience of European manufacturers
has shown that such batteries are economical, and we
have finally come round to using paste plates for
this work, but about ten years behind the practice in
Europe.

126. Negative Plates. — Only a few manufacturers
use the true Plants type of negative plate for any
service whatever. The Gould plates are the only
pure Plante negatives in. general use in this country.
The negative differs from the positive in having thin-
ner ribs, and a thinner center web, and in having a
much larger percentage of the whole weight in the
form of active material. It is made by formation as
positive first, and the rapid forming process is carried
on until the lead of the original blank is nearly all
changed to peroxide, just enough being left to hold
the plate together. ' There is no danger of the plate
ever getting any weaker after it goes into service, for
once it lias been reversed to the negative condition
there will never be any further action on the lead of
the support plate.

Paste Negatives. — The commonest type of negative
plate for general service is a paste plate. It differs
from the negatives used in electric automobiles only
in being more heavily constructed. The grids for

SOME COMMERCIAL TTPE3

287

these plates are usually made with the dovetails of
the strips expanding outward to give the active ma-
terial, which contracts in service, an opportunity to
keep in good contact with the grid. I am not at all
Bure that this is anything more than an inherited
idea, but it seems to be followed universally by
manufacturers of paste negatives.

Box Negative. — The Plants negative is peculiar in
ita ways, and not always easy to control. The paste
negative has not the ex-
tremely tough constitution
necessary for some of the
modern high-rate regulation
work. As a mean between
the two, and with the inten-
tion of avoiding, if possible,
the troubles of both the other
types, what is called the
"box" negative has been de-
veloped, and put into active
service both in Europe and i
shown in Figure 91, and it consists of a frame of
antimony lead into which are put the blocks of active
material. A front and back cover, both full of tine
perforations, complete the plate. The active ma-
terial is prepared in the form of blocks which fit the
openings in the frame. Some manufacturers have
sent them out into service without any preliminary

1 this country.

238 8T0BA0E BATTERIES

formation, the charge necessary for the development
of the positives being just about sufficient to form
the very porous active material of the negative. It
is usually considered better to form them before
sending them out.

At first sight it seems like a decided step backward
to place active material inside a box, forcing diffusion
to take place through small openings. But the much
more difficult diffusion through the fine pores of the
material inside the perforated cover completely over-
shadows any effect of the outside cover. Further-
more, the presence of the cover permits the maker to
use a very porous active material indeed. It need
have no coherence in the mechanical sense as long as
it has conductivity, and the latter property is aided by
adding finely divided carbon to the prepared block.
The increased porosity which can be attained in this
way more than makes up for the longer diffusion
path through the perforations in the plate.

127. Submarine Cells. — Next in order of size after
the central station and regulating batteries come
the ones used in submarine boats. Here the design
is most exacting, for both space and weight are
sharply limited, especially the former, and a very
large amount of power must be furnished over a con-
siderable time. Paste plates are .the rule, and the
average size is about 15 x 24 in., and from 21 to 35
plates to the cell. The containing tanks are of hard

SOME COMMERCIAL TYPES 239

rubber, — much like giant vehicle cells, — and they
are fitted with arrangement for disposal of all gases
formed during operation. The mixture of hydrogen
and oxygen which is produced in the cell is about as
sharply explosive as anything possibly could be, and
serious accidents have resulted from faulty gas dis-
posal and ventilation. The best way seems to be to
fit each cell with its own tight cover and with escape
pipe, rather than to shut up the cells in a gas-tight
compartment, which is freed from gas by a fan.

The plates for this service are made to have a
capacity as high as is compatible with a reasonable
life. Tests include not only capacity at various rates
of discharge, but also tests for mechanical strength,
and a discharge while the cell is being rocked rather
violently through an angle of about 30°.

Of course the boat is dependent wholly on its
batteries for power while submerged. Sixty cells
must give about 5000 ampere-hours at the 3- or
4-hr. rate. Even this only means

l^i<^= about 250 H.P.,
3 X 746

which is not a very large amount of power to drive
a boat as large as a modern submarine.

128. Train-lighting and Car-lighting Service. — In
Denmark cars have been carrying batteries for light-
ing service for more than twenty years, and they have

240 STORAGE BATTERIES

found this application a valuable one. This branch
of storage battery engineering has been of increas-
ing importance in this country in the past few years.
Some day before long it will be statutory that every
railroad train shall do all its lighting by electricity.

The simplest system is ** straight battery." The
charged battery is taken on at one terminal, dis-
charged at a rather low rate during the trip, — at the
24-48 hr. rate — and removed at another point, a
freshly charged battery taking its place. There is
much of this practice in the United States. The
regular cell for this work can give about 250 to 350
ampere-hours. Sixty cells in a battery give an aver-
age of 110 volts, and will run 60 16-candle-power
lamps for 24 hr.

Car-lighting Systems. — Often an axle-driven dynamo
is added, which can furnish somewhat more than
power enough to run all the lamps when the train is
moving at a speed greater than thirty miles per hour.
The excess energy is absorbed by the battery when
the train is running at higher speeds than this, and
the battery must run the lights while the train is
standing still. Usually a complete system of regula-
tion is provided, so that the battery acts just as a
large regulating battery would in a power plant —
absorbing energy whenever an excess is being turned
out by the dynamo and giving it out again at the
times when the speed is low or the car is standing still.

SOME COMMERCIAL TYPES 241

Train-lighting Systems. — In through trains which
make a run of many hours without change in make-up,
the generator for the whole train is sometimes in-
stalled on the locomotive and driven by a steam tur-
bine. A regular " booster " outfit is installed either
on the tender or in the baggage car, and this attends
to regulation of all load variations. The battery in-
stalled in each car is sufficient in capacity to run its
own lights for a time, and the train can therefore be
made up and broken up without interruption in ser-
vice. As soon as the train has been made up, the
generator takes the load and the batteries are kept
nearly fully charged. They then have to care only
for the regulation and to serve as reserve.

In all of these different kinds of lighting service,
the pure Plante plates have done well, and most of
the companies wlio do this work make special Plante
type plates for it.

129. Vehicle Service. — A rapidly growing field of
usefulness for the storage battery is in vehicle
service. At first glance it seems a poor substitute
for the light and efficient internal combustion
engines of modern times. To drive a pleasure
vehicle at a reasonable speed over average streets
and good roads requires about 1.5 KW. If the
battery has 32 cells, its average voltage during dis-
charge will be 60, and each cell must be able to
give 25 amperes for four or five hours. Such a bat-

242

BTOBAQE BATTBRIES

tery will cost about $250, and will weigh not far
from 750 lb. complete.

But this electric vehicle has many important ad-
vantages. It is clean and neat, it is simple to oper-
ate, and it is almost absolutely certain to go if there
is a charge in the battery.
Where a central charging
station can arrange to
charge many batteries each
night, tlie whole arrange-
ment is eSicient and eco-
nomical. It is ratherstrange
to see how the heavy truck,
driven by electricity and
doing its hard work day
after day, has been the best
of arguments with which to
convince the doubter of the
economy of the electric ve-
hicle in light work and for
pleasure.

Tlie plates used in vehicle work are legion in name
and varied as to fame. Paste plates are now almost
universally used over the world. European practice
runs toward thinner and lighter plates, cheaply made
and with a limited but well understood life. In this
country we make heavier and stronger plates of
lower weight capacity, but having longer life.

1. 92. — Paste vehicle Etid. '

SOME COMMERCIAL TYPES 243

Wbioht Efficibmct of Paste Batteries
American StancUrd Plates 71-81 watt-hours per pound

American Light, high capacity, 101 watt-liours per pound
Edison 121 vatt-hours per pound

Medium European 11 watt-houra per pound

Light European 14 watt-houis per pound

Figures 93 and 94 show one of the commoDest
types of grids used in makiog vehicle plates. Most
positive grids are so made as to give support from
outside to the rather loose and noncoherent per-
oxide. This support is supposed to be
given by making the ribs of the cross-
section shown in Figure 76. The neg-
ative grid is made with its dovetail in
the opposite sense, as already explained.
Many complicated forms of grid have
been patented and used, but gradually
the majority of manufacturers have
settled down to the similar ty^ws.
The old original ideas are sure to recur Fio, 93. — Cross-

. Bcction of mold

at fairly regular intervals, sometimes and grid cut-

beoause the cause of trouble has been ^^'
removed, and sometimes because it has been forgotten.
About the only decided variation from the simple
grid type now in evidence is the so-called "iron-
clad" vehicle plate (Figure 95). The type is pe-
culiar in depending on an insulating support grid or
envelope of rubber, celluloid, porous biscuit ware,

2-H STORAGE BATTERIES

wood, etc. This surrounds the active material and
prevents shedding, and contact is made witli a cen-
tral lead strip or wire. Tliere seems every reason
to believe that the apparent
tj security is not a very real

"i^_^; -i— 1 ^'^^' "" '^ quit« possible

^^^^= =1 for positive active material

^^^^^ g to lose coherence and ca-

F^^^^^ gi pacity even though the ma-

^E =^^^ g ! terial cannot get away and

— ■ fall to the bottom of the

cell, as it does in the or-
dinary ease.

This particular plate
has, however, been care-
fully tested by the makers,

=^l^Mj and may prove an excep-
■ '■■''■■" tion to the rule.

The present status of
the vehicle battery might
be summarized as follows: There is not very much
difference in standard plates by different makers.
Grids differ but slightly. Formation and other treat-
ment is becoming a well-known art. With proper
operation the good American battery should give
250 to 400 cycles without much trouble. It must
be cleaned once during this life, probably after 200
to 300 cycles.

SOME COMMERCTAL TYPES

If operating con-
ditions are not right,
the same battery
may begin to givi
trouble after 10(
discharges or less
I know of one com
pany which man
ages to get nearly
450 cycles in haii
service from any oni
of several of thi
standard Americat
types.

A set of vehiclt
negative plates is
usually assumed to
outlast two sets of
positives. This is
usually conserva-
tive. Fio. 95,-

— I

" IroD-clad " vehicle plate.

248 STORAGE BATTERIES

lead sulphate has almost too great solubility in sul-
phuric acid, for negative plates lose in capacity be-
cause of the increase in the size of lead grain. Lead
peroxide is ideal in this respect.

A reaction must be selected which yields a large amount
of energy per gram equivalent of material used. While
the substances used in the lead cell are unfortunate
by reason of their high equivalent weights, Ihey are
fortunate in another way. Energy is obtained not
only from the anode reaction, where lead goes into
solution, but also from the PbOj reaction. Lead
peroxide is one of the electrodes which can furnish
energy during reduction.

The cell must have a low internal resistance, otherwise
its efficiency will be impaired. Again the lead cell is
a fortunate choice, for hardly any electrolyte has a
lower specific resistance than 30 % sulphuric acid, and
both lead and lead peroxide are good conductors.

The chemical reaction must be perfectly reversible. The
losses in the lead cell are almost wholly due to the
production of gas.

132. The first efforts toward the discovery of a
cell other than Plant^'s start from his work and from
his point of view, as would be expected. Peroxide
of lead has been tried with most of the metals replac-
ing lead as the other plate. Zinc, cadmium, copper,
bismuth, etc., were all given a trial, and no one of
them has proven better than lead. Then, too, the

ACCUMULATORS IN GENERAL 249

alkaline combinations, starting with the Lalande-
Chapeyron type, were given a trial. The following
may be mentioned : —

Copper /potassium hydroxide /silver peroxide.
Cadmium /potassium hydroxide/copper oxide.
Ziuc/potassium hydroxide /copper oxide.
Iron oxide/potassium hydroxide/manganese dioxide.
Iron (?) /potassium hydroxide/nickel peroxide.
Cobalt/ potassium hydroxide/ nickel peroxide.

I. Until recent years the lead-sulphuric acid
cell has had the commercial field to itself. A great
many suggested combinations were tried, but no one
of them has stood the test. Usually it has been the
mechanical reversibility which has been at fault,
even when the chemical reaction has been a favorable
one and quite reversible.

Lately one combination has been developed which
bids fair to make a place for itself in practical serv-
ice. It is already a success as far as all tests of
reversibility, mechanical and chemical, are concerned.
This is the iron/potassium hydroxide/nickel per-
oxide cell, as developed by Edison to mechanical
perfection in this country. Figure 96 shows an
assembled cell. The cell and support plates are made
of nickel steel. The perforated hollow tubes of the
positive plate (see Figure 97) contain a mixture of
metallic nickel and nickel oxide before development.
After development the active material is perhaps

250

STORAGE BATTERIES

NiOy the peroxide of uickel. In the finely perfo-
rated flat boxes of the other plate (aee Figure 98) is
a mixture of iron, iron oxide, and lampblack. This
is the negative plate,
and on charge metallic
iron seems to be formed
in part. Tbe electro-
lyte is concentrated
caustic potash solution.
There is still much
to be learned about the
fundamental cell re-
action. The simplest
formula is

NiOj+Fe = NiO-|-FeO,

and tilts is a fairly close
statement though not an
accurate one. This for-
mula indicates one inter-
esting point. The elec-
trolyte does not appear
Fio. 90. — Edison cell. at all. And it is quite

true that the change in
the density of the electrolyte, from complete charge
to complete discharge, is small. There is a slight
change of concentration, but not sufficient to be of
service as an indication of the condition of the cell.

ACCUMULATORS IN OENEBAL

251

It is of course perfectly certain that there are
changes of concentration of the electrolyte in the
active part of the plates, and that theae
changes are proportional to the rate at
which the cell ia working. It is quite
certain that the effect of diffusion,
which has heen called on so often in
explanation of the course of charge
and discharge curves
of lead cells, playa just
as important part in
the Ediaon cell. Until
wo know just what the \ i
fundamental cell reac-

Fio. 87.— Group tion IS, wc cannot fore-
tive plates. ^^^ i^^^ '"'^^ great the

effect of change in the
0H~ concentration will be.

There are many interesting things
about the curves taken on this type ot
cell. Figure 99 shows discharge curve Pio. 98.— Group
to a low voltwre, much lower than of Edison nega-

^ _ tive plates,

would be reached in practice. The

evident two stages in the curve, without any change
in the distribution of active material to account for it,
may mean a change in the cell reaction at that point.
This particular type of cell has the following
characteristics at 25° C. : —

8T0BAGS BATTEBIES

Fto. 00. — Discbarge ci

:::^

d"^

s=\

IJU

Fio. 100. — Discharge c

ACCUMCLATORS IN GENERAL

■-^

-1

■\

■^

'lo. 101. — Discharge curvea of Edison call at van
Weight ot complete cell, 19.25 lb8.
Capacity

IB temperatuns.

[ampere-hours, 225.
I watt-hours, 248.

■■

■

TCmiUTUnEfCWTOUIX)

Fio. 102. — Summary showiog change in
ampere-hour capacity with temperature.
(Exide and Ediaon.]

Ampere-houts per
pouDil of cell, 11.3.

Watt-hours per
pound of cell, 12.4.

Ampere-hour ef-
ficiency, 82%.

Watt-hour effici-
ency, (30 % .

An examination
of the temperature
effect shows the im-
portant part which
diffusion plays in
the cell activity.

254

STORAGE BATTERIES

The curves of Figures 100 and 101 show the relative
temperature effects on a standard type of lead cell

and on an Edison
cell, and these are
summarized in the
curves of Figures
102 and 103.

The factors which
determine the prac-
tical success of such
a cell are numerous.
Without any inten-
tion of either criti-
cizing or advertis-
FiG 103. -Change in watt-hour wacity i^g, we can examine

with temperature. [Exide and Edison.] ^

the general charac-
teristics of some present^ay types. The following
table gives data on three types — a rather heavy
American plate, a rather light European type, and
the regular Edison type of approximately the same
watt-hour capacity.

10* ao* dof

tempcraturcCccntigrak'^

Watt-hours per pound

Life

Cost

Watt-hour efficiency .

Standard

LiUIIT

Amkrioan

EVKOPCAM

75%

80%

Edison

12.5
3

21
60%

APPENDIX

The General Equation for the Electromotive Force of a Cell
in Terms of the Heat of the Chemical Reaction and the Tem-
perature Coefficient of the Electromotive Force

Assume

1. The law of the conservation of energy.

2. The second law, in the form

work done

heat used in doing it T

We send our cell through the following cycle : —

1. At temperature T, send 96,540 coulombs through
at e volts. The work done is Fe joules.

Suppose the cell cool while it works. It will
absorb TT calories from its surroundings. W^eF— Q^
Q being the chemical heat of reaction.

2. Raise the temperature of the cell to T -\' dT.
This will take P calories. The electromotive force
is changed io e -{• de.

3. Now send 96,540 coulombs through in the oppo-
Bite direction^ against e -{• de volts. The work done
is F(e + de) joules. The cell heats when it works

256

256 STORAGE BATTERIES

in this direction. It gives out W -\- dW calories.
W-h dW^ F(e + de)-lQ + rf^].

4. Cool the cell back to T. We get back our
P calories.

dW a,nd dQ are vanishingly small. They can be
neglected, since (22^ is an infinitesimal temperature
difference.

The net result of this cycle is an amount of avail-
able work Fde> To produce this amount of available
work, a quantity of heat Fe — Q changed its temper-
ature from T-{- dT to T.

Apply the second law.

_Fde_^dT

Fe- Q T'

Transforming,

dl'

Calculation of the Electromotive Force of a Cell in Terms of
the Solution Pressure at the Electrodes and the Osmotic
Pressure in the Solution

Assume the gas law to hold for osmotic pressures.
pv = RT.

p = osmotic pressure.
V = volume of a gram-molecule.
It = gas constant.
T — absolute temperature.

APPENDIX

257

The work obtainable by a change in concentration
from/?i to;?2 *^ constant temperature is

Solution pressure is continually balanced at the
electrode by osmotic pressure and work done is
osmotic work.

A^RTln^ — where P is solution pressure, ;? is

osmotic pressure, and A is work done at the single
electrode.

We are calculating in gram-molecules. For a
univalent ion, 96,540 coulombs will pass the cell with
a gram-molecule ; and g, the electromotive force, will
be a measure of A^ the work done at the electrode.

For a univalent ion

RT, P

e = — =-ln- — .

F ' p

If the ion which maintains equilibrium is bivalent,
only half as much of it need pass the electrode to
carry the 96,540 coulombs, and if it is n-valent,
J_
nth

as much will be enough.

For an n-valent ion we have

RT. P

e = — - In, — .

7iF p

258

STORAGE BATTERIES

At the other electrode we have a precisely similar
equation to express the action, but here the ion
passes the electrode in the opposite direction and e
has the opposite sign. The electromotive force of
the whole cell will be the difference of the two single
electromotive forces.

BT .
F

is constant at constant temperature. Its nu-

merical value at 17° C. is

8.31 X 290 X 2.303
96,540

= 0.0575.

We have introduced the factor 2.303 which changes
natural logarithms to common. The equation as
usually applied is

e =

0.0575

log

P. P.

Pl'P2

III

Calculation of the Concentration of the Active Ions in the Lead

Accumulator

(1) The concentration of Pb"^^ ion.
The solubility of lead sulphate in pure water is
1.4 xlO-* gm.-mol. per liter. Assuming complete

APPENDIX 269

dissociation and that the mass law holds for ionic
equilibrium, we have

Pb++ . SO^-- =(1.4 X 10-*)a = 1.96 x 10-8.

Accumulator acid is about 2 N but is only about
50% dissociated. In this acid SO^ is therefore
1.0 JV, and in the cell

Pb++ = 2 X 10"8 gm.-mol. per liter.

(2) The concentration of H"*" ion.

As stated above, 2 N H^SO^ is about 50 % dis-
sociated, the concentration of H"*" is therefore about
2 gm.-mol. per liter.

(3) The concentration of PbOj ion.
From the mass law : —

PbOj— = Pb++ . (0~)a
and (H"*")^ • O = constant.

Therefore,

PbO«~~ = constant -rrrrri'

The value of the constant can be calculated by
measurements of the solubility of lead hydroxide in
sodium hydroxide solution, and these measurements
are within tlie range of analytical attack. In Dola-
zalek's determination the sodium hydroxide was
0.066 normal, and it dissolved Na^PbOj to a concen-
tration of 0.00305 gm.-mol. per liter. In this

260

STORAGE BATTERIES

solution PbOj was therefore about .003 JVand the
remanent alkali contained 0.054 gm.-mol. 0H~ per
liter.

The concentration of H"*" in this solution we can
calculate with the aid of the mass law. We have

H+ . OH— = 1.1 X 10-1*

from measurements on water, gas cells, etc.

In our alkali solution, OH" is about .05 normal.

H+ is therefore about 2 x lO-^^ JV.

The lead ion concentration in the alkali we need
also. In pure water, lead hydroxide dissolves to
about 4 X 10"* gm.-mol. per liter.

We have

Pb++ . (0H-)2 = (4 X 10-*)8 = 6 X 10-",
and for our .05 JV alkali

6 X 10-11

Pb++ =

= 2 X 10-«.

(.05)2

Now we can calculate our constant

y^ PbO." • (H-^)*
Pb++

y _ (3 X 10-8) . (-1.6 X 10-*')

2 X 10-8

2r= 3 X io-«.

From this, for 2 N acid

PbO,~ = 3xlO-«.^^.

APPENDIX

261

From (1) Pb++ = 2xl0-8.
From (2) H+ = 2.
(H+)*=16.

FinaUy PbO,- = « >< ^^^^^^^ >< l^"^.

PbOj— = 4 X 10-«

This is the concentration of the PbO^ ion in the
ordinary lead cell, using as electrolyte 2 ilTacid.

Variation in Capacity with Volume of Electrolytd

An important factor in the design of a storage cell
is the permissible volume of the electrolyte. It is

L2J 60

\Z 70

U9^60

UTJ^SO

§ I

U5 40

M3 30

fc^ . .

—

1 4

> c

\ 1

' c

\ s

» l«

HOURS

Fio. 104. — Variation in capacity with volume of electroljrte.

A, capacity with 2000 cu. cm. of electrolyte, at various rates,
a, density of electrolyte corresponding to A.

B, capacity with 1100 cu. cm. of electrolyte.
/I, density corresponding to B.

262 STORAOS BATTERIEa

quite evident from general considerations that in a
cell containing many plates and little electrolyte,
the latter may limit capacity by becoming so dilute
that the useful working volt^e is soon passed.

Figure 104 shows the capacity of a cell and the
change in the density of the cell electrolyte at differ-
ent ratea of discharge and with different volumes of
electrolyte in the cell.

The Gsa given off from the Lead Cell

A mixture of oxygen and hy-
drogen is given off from a lead
accumulator during the latter
part of charge. This is a very
, explosive gas mixture, and in
submarines and other places
where batteries are closely con-
fined, ventilation must be very
carefully looked out for.

Figure 105 gives a diagram-
matic picture of apparatus which
can be used to measure the rate
at which gas is evolved during
charge and discharge. The gas
^noiTo^m^riT escapes through the narrow cap-
rate of evolution of gas. illary, and the gas pressure is
measured by the small mercury manometer.

APPENDIX

268

Figure 106 gives curves of a test on the rate of
gassing of paste and Plante negative plates during
charge at the 8-hr. rate.

3 4

HOURS OF CHARGE

Fio. 106. — Curves showing evolution of hydrogen from paste and

Plaut6 negative plates during charge.

Specific Resistance

Aluminium 3 x 10"'

Lead 2 x lO""

Copper 1.7 X 10-«

Graphite (about)
Quartz ....
30 % HjSO^ . .
31% IINOj . .
20 % HCl . . .

6 X 10-8

3xlOK>

1.4

1.3

INDKX

Accumulators, general considora-

tions, 246.
Acid density during charge and

discharge, 44.
Auxiliary electrode, use of, 114.

Box" negative, 237.

Capacity, 116.

and acid density, 134, 166.

and Faraday's law, 1 17.

and plate thickness, 122, 123.

and temperature, 134.

and volume of electrolyte, 261.

calculations, 124.

change in, during service, 193.

curves, theoretical, 119, 125.

determined by end voltage, 118.
Car-lighting systems, 240.
Cementing of pastes, 196.
Charge curve, at various rates, 102.

complete, 98.

first part of, 97.

peculiarities, 99.

various types, 103.
Charge and discharge, 94 et acq.
Charge and discharge curves,

individual plates, 114.

various rates, 112, 113.

various tyi>es, 109.
Charge and discharge voltages
(average) at various rates,
146.
Charge reaction, 41.
Chemical potential, 22.
Commercial types, 225.
Current density, possible changes
at high, 40.

Daniell cell, 19.
Definitions of all parts, 1 1 .
Deformation (buckling, etc.), 215.
Densities of lead compounds, 175.
Diffusion curves and recovery

curves, 131.
Diffusion, general discussion, 129.

in resting plates, 129.

Liebenow's experiment, 129.
Discharge curve, and acid density,
107.

at various rates, 120.

first part of, 105.

to low volleys, 110, 111.

various types, 121.
Discharge reaction, 49.
Diseases and troubles, 207, 213.

Edison cell, 250.

characteristics, 253.

discharge curves at various
temperatures, 253.
Efficiencies at various rates, 144.
Efficiency, ampere-hour, 141.

energy, 143.
Electrical energy, 25.
Electrical units, 13, 24, 25.
Electro-chemical unit, 21.
Electrode, standard, 82.
Electrode equilibrium, 86.
Electrode reactions, 81.
Electrolytic cell, 13.
Electromotive force, 22.

and acid density, 77.

theory, 256.
Electrostatic equilibrium about

an electrode, 62.
Energy relations, 64.

265

266

INDEX

Faraday*8 law, 11, 15.
Formation at low voltage, 188.

Plant*, 179 el seq.

rapid Plant*, 184.

theory of, 186.
Forming agents, 185.

persistence of, 191.
Fundamental energy equations,

67, 70, 255.
Fundamental reaction formula, 40.

Gas evolved from lead cell, 263.
General equation for electro-
motive force, 255.

Heat of dilution of sulphuric
acid, 74.

Impurities and local discharge, 217.

effect of, 208, 212.
Ionic concentrations, calculation

of, 258.
Ionic theory, 33.
Ion reactions, 38.
Ions, 12, 23, 30 ei acq.

active, during charge and dis-
charge, 50 et seq.

in electrolyte, 48.
••Iron-clad" plate, 245.

Lead cell reaction, 39 et acq,
Le Blanc's theory, 89.
Liebenow's theory, 90.
Load regulation, 229.

Migration of ions, 36.
Migration velocities, 35.

Non-lead types, 249.

Operation of batteries, 223.
Osmotic theory of galvanic cells,

256.
Osmotic work, 86.

Paste negatives, change during
formation, 204.

Paste plates, 194.

Paste positives, formation, 198.

types, 237.
Paste recipes, 202.
Physical characteristics, 172.
Plant* negatives, 192, 236.
Primary cells, 3.

Reaction velocity, 136.
Recovery, after charge, 104.

and diffusion, 131.

after discharge, 107, 108.

after long discharge, 133.
Resistance, 27.
Resistance curves, 153 ei seq.

factors of, 155.

of sulphuric acid solutions, 149.

specific, 148, 263.

temperature effect during activ-
ity, 165.

temperature effect on, 151.
Restoring capacity of negatives,
214.

Self-discliargeof Plant* plates, 183.
Shedding of active material, 218.
Short circuits, 219.
Solution pressure theory, 84.
Stand-by batteries, 232.
Submarine cells, 238.
Sulphation, 216.

and internal resistance, 157.

Temperature coefficient of electro-
motive force, 72.
Thermochemical data, 66.
Train-lighting systems, 241.

Vehicle grids, 242.
Vehicle service, 241.

Watt-hour capacity, 137.

at various temperatures, 139.

diagrams, 138.
Weight capacity, 243, 254.
Work done at an electrode, 64.
Work, osmotic, 86.

UNIV. OF MICHIGAN,

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obtained unless arbitrary rules of multiplication and division are
introduced. It therefore is necessary thoroughly to examine the
fundamentals of these uses of complex quantities, and to deduce
the laws of addition, subtraction, multiplication, and division, as
applicable to vector quantities and to harmonic quantities whether
simple (electromotive force or current) or compound (power),
and also to such non-harmonic quantities as resistance, capacity,
inductance, etc., in connection with harmonic quantities.

THE MACMILLAN COMPANY

Pnblithers 64-66 Fifth Avenue New York

Magnetism and Electricity for Students

By H. E. HADLEY, B.Sc. (Lond.)

Associate of the Royal College of Science, Tendon ; Headmaster of the

School of Science, Kidderminster.

579 pogesy $1.40 net

The Storage Battery

By AUGUSTUS TREAD WELL, Jr., E.E.

Clothy 257 pagesy $1.7$

An aid to those who have direct charge of storage batteries, and
to those who are interested in their workings.

An Elementary Book on

Electricity and Magnetism and Their Applications

By DUGALD C. JACKSON

Professor of Engineering, Massachusetts Institute of Technology, and

JOHN PRICE JACKSON

Professor of Electrical Engineering, Pennsylvania State College.

New York, 1907.

Cloth y I2m0y 482 pages y $1.40 net

The author begins with a treatment of the theoretical considera-
tions of electricity and magnetism, presenting them in an elemen-
tary descriptive manner. The theory is then developed and the
practical applications of it to electric machinery are given. The
book will serve as an excellent introduction to Engineering courses.
It has also proved to be valuable in the hands of students wishing
to make a hasty review of the whole subject at the close of their
Electrical Engineering course.

THE MACMILLAN COMPANY

Pnbliih«ra 64-66 Fifth Avenne Hew York

The Elements of Electrical Engineering

A Text-book for Technical Schools and CoUeges
By WILLIAM SUDDARDS FRANKLIN

Professor of Physics in Lehigh University, and

WILLIAM ESTY

Professor in Electrical Engineering in Lehigh University. New York, 1907.

TWO VOLUMES

L Direct Current Machines Cloth^ 8vo, 517 pages, $4.50 net

n. Alternating Currents Clolh, 8vo, 378 pages, $3.50 net

Volume I, published in July, 1906, has become in the two years that
it has been upon the market one of the most widely used texts on the
subject now published. It has given universal satisfaction as a treat-
ment easily understood by the students, and yet thorough and complete
in detail.

Volume II, published in 1908, promises to be equally satisfactory.

•

Electric Waves

An Advanced Treatise on Alternating-Current History
By WILLIAM SUDDARDS FRANKLIN

Professor of Physics in Lehigh University.

31S pages, $3.00 net

"The author states that as it is most important for the operating en-
gineer to be familiar with the physics of machines, the object of this
treatise is to develop the physical or conceptual aspects of wave motion,
that is, " how much waves wave," and that, with the exception of the
theory of coupled circuits and resonance, it is believed that the "how
much " aspect of the subject is also developed to an extent commensu-
rate with obtainable data and the results derived from them. While
this treatise is stated to be complete both mathematically and physi-
cally, as far as it goes, the student is referred to other works for the
more elaborate mathematical devolopments." — Proceedings of the
American Society of Civil Engineers,

THE MACMILLAN COMPANY

Pnblishers 64-66 Fifth ATeniw Hew Tork

Applied Electrochemistry

By M. DE KAY THOMPSON, Ph.D.

Assistant Professor of Electrochemistry in the Massachusetts Institute

of Technology

Cloth, 8vOf 32g pages, index, $2.10 net

This book was written to supply a need felt by the author in
giving a course of lectures on Applied Electrochemistry in the
Massachusetts Institute of Technology. There has been no work
in English covering this whole field, and students had either to
rely on notes or refer to the sources from which this book is com-
piled. Neither of these, methods of study is satisfactory, for notes
cannot be well taken in a subject where illustrations are as impor-
tant as they are here ; and in going to the original sources too
much time is required to sift out the essential part. It is believed
that, by collecting in a single volume the material that would be
comprised in a course aiming to give an account of the most im-
portant electrochemical industries, as well as the principal applica-
tions of electrochemistry in the laboratory, it will be possible to
teach the subject much more satisfactorily.

The plan adopted in this book has been to discuss each subject
from the theoretical and from the technical point of view sepa-
rately. In the theoretical part a knowledge of theoretical chem-
istry is assumed.

Full references to the original sources have been made, so that
every statement can be easily verified. It is thought that this will
make this volume usful also as a reference book.

An appendix has been added, containing the more important
constants that are needed in electrochemical calculations.

THE MACMILLAN COMPANY

Fnblishen 64-66 TifUt Avenne Hew Tork

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